In the New Testament, our peace offering is Christ. We no longer offer burnt offerings, but instead we remember the offering of Christ in the Eucharist, which means "Thanksgiving," which we usually call the "Lord's Supper" or "Communion" in the Reformed churches. In the Old Testament, however, there was an option to offering a peace offering as a thanksgiving to God. The following passage provides the mechanism for a person to offer thanks to God then:
And this is the law of the sacrifice of peace offerings, which he shall offer unto the LORD. If he offer it for a thanksgiving, then he shall offer with the sacrifice of thanksgiving unleavened cakes mingled with oil, and unleavened wafers anointed with oil, and cakes mingled with oil, of fine flour, fried. Besides the cakes, he shall offer for his offering leavened bread with the sacrifice of thanksgiving of his peace offerings. And of it he shall offer one out of the whole oblation for an heave offering unto the LORD, and it shall be the priest's that sprinkleth the blood of the peace offerings. And the flesh of the sacrifice of his peace offerings for thanksgiving shall be eaten the same day that it is offered; he shall not leave any of it until the morning.
It is interesting to note that the peace offering was accompanied by both unleavened cakes and leavened bread. This suggests that both leavened and unleavened bread may be suitable for our thanksgiving in the Lord's Supper, despite the long-standing disagreement between the Greeks and the Romans.