Into a large pot of boiling water, using tongs, dip cabbage leaves into water until blanched, about 30 seconds. Transfer to a paper towel–lined plate to dry.

In a large skillet over medium heat, heat 1 Tbsp. oil. Add bell peppers, onion, and oregano; season with salt and pepper. Cook, stirring often, until onion and peppers are tender, about 7 minutes. Transfer to a plate. Add remaining tablespoon oil to skillet.

In same skillet over medium-high heat, heat remaining 1 Tbsp. oil. Arrange steak in a single layer; season with salt and pepper. Cook, undisturbed, until steak is seared on one side, about 2 minutes. Flip and cook until the steak is seared on second side and cooked to your liking, about 2 minutes more for medium.

Return onion and peppers to skillet and toss to combine. Top with an even layer of provolone and cover skillet with a tight-fitting lid. Cook until cheese is melty, about 1 minute.

Scoop some steak mixture onto the center of a cabbage leaf. Fold short end of leaf over, then roll up the long side like a burrito with an open end. Repeat with remaining leaves and steak mixture.