Luke 6

Luke 6:3

"And Jesus answering them said, "Have you not even read what David did when he was hungry, he and those who were with him,"
Did Jesus actually break the OT law?

Jesus is accused of both violating the Sabbath and stealing corn. Once again, however, he is violating a Pharisaic interpretation of what constituted "work", not an actual OT law, and his picking of corn from the fields of the others is allowed in the OT (Lev. 19:9-10) and is not considered to be stealing.