Commenting on Leviticus 1 & Leviticus 3:
“There is something more in the peace-offering than the abstract devotedness of Christ to the will of God. The worshiper is introduced; and that not merely as a spectator, but as a participator—not merely to gaze, but to feed. This gives very marked character to this offering. When I look at the Lord Jesus in the burnt-offering, I see Him as One whose heart was devoted to the one object of glorifying God and accomplishing His will; but when I see Him in the peace-offering, I find One who has a place in His loving heart and on His powerful shoulder for a worthless, helpless sinner. In the burnt-offering, the breast and shoulder, legs and inwards, head and fat, were all burnt on the altar—all went up as a sweet savor to God; but in the peace-offering, the very portion that suits me is left for me. Nor am I left to feed in solitude on that which meets my individual need. By no means. I feed in communion—in communion with God, and in communion with my fellow-priests. I feed in the full and happy intelligence that the self-same sacrifice which feeds my soul has already refreshed the heart of God; and, moreover, that the same portion which feeds me feeds all my fellow-worshipers. Communion is the order here—communion with God—the communion of saints. There was no such thing as isolation in the peace-offering. God had His portion, and so had the priestly family.
Thus it is in connection with the Antitype of the peace-offering. The very same Jesus who is the object of Heaven’s delight, is the spring of joy, of strength, and of comfort to every believing heart; and not only to every heart in particular, but also to the whole Church of God in fellowship. God, in His exceeding grace, has given His people the very same object that He has Himself. ‘Truly our fellowship is with the Father, and with His Son Jesus Christ’ (1 John 1). True, our thoughts of Jesus can never rise to the height of God’s thoughts. Our estimation of such an object must ever fall far short of His; and hence, in the type, the house of Aaron could not partake of the fat. But though we can never rise to the standard of the divine estimation of Christ’s Person and sacrifice, it is nevertheless the same object we are occupied with, and therefore the house of Aaron had ‘the wave breast and the heave shoulder.’ All this is replete with comfort and joy to the heart. The Lord Jesus Christ, the One ‘who was dead, but is alive for evermore,’ is now the exclusive object before the eye and thoughts of God; and, in perfect grace, He has given unto us a portion in the same blessed and all-glorious Person. Christ is our object too—the object of our hearts and the theme of our song. ‘Having made peace by the blood of His cross,’ He ascended into heaven, and sent down the Holy Ghost, that ‘other Comforter,’ by whose powerful ministrations we feed upon ‘the breast and shoulder’ of our divine ‘Peace-offering.’ He is indeed our peace; and it is our exceeding joy to know that such is God’s delight in the establishment of our peace, that the sweet odor of our Peace-offering has refreshed His heart. This imparts a peculiar charm to this type. Christ as the Burnt-offering commands the admiration of the heart; Christ as the Peace-offering establishes the peace of the conscience, and meets the deep and manifold necessities of the soul. The sons of Aaron might stand around the altar of burnt-offering; they might behold the flame of that offering ascending to the God of Israel; they might see the sacrifice reduced to ashes; they might, in view of all this, bow their heads and worship; but they carried naught away for themselves. Not so in the peace-offering. In it, they not only beheld that which was capable of emitting a sweet odor to God, but also of yielding a most substantial portion for themselves, on which p 308 they could feed in happy and holy fellowship.
Assuredly it heightens the enjoyment of every true priest to know that God (to use the language of our type) has had His portion ere he gets the breast and the shoulder. The thought of this gives tone and energy, unction and elevation, to the worship and communion; it unfolds the amazing grace of Him who has given us the same object, the same theme, the same joy with Himself. Nothing lower—nothing less than this could satisfy Him. The Father will have the prodigal feeding upon the fatted calf, in fellowship with Himself. He will not assign him a lower place than at His own table, nor any other portion than that on which He feeds Himself. The language of the peace-offering is, ‘It is meet that we should make merry and be glad’—‘Let us eat and be merry.’ Such is the precious grace of God! No doubt we have reason to be glad, as being the partakers of such grace; but when we can hear the blessed God saying, ‘Let us eat and be merry,’ it should call forth from our hearts a continual stream of praise and thanksgiving. God’s joy in the salvation of sinners, and His joy in the communion of saints, may well elicit the admiration of men and angels throughout eternity.” C. H. Mackintosh, Genesis to Deuteronomy: Notes on the Pentateuch. (Neptune, NJ: Loizeaux Brothers, 1972), 307–308. [Italics original.]
*I am indebted to my friend & brother in Christ, Mr. John Morell, for alerting me to this excellent quotation.  -KRK