Preheat the oven to 400?F.

Slice about a third off the top of each pepper and remove the ribs and seeds. Leave the stems on and slice the tops into thin strips.

Place the peppers cut side-up in a baking dish and bake for 30 minutes.

Heat 2 tablespoons olive oil in a large skillet or griddle over medium heat. Add the reserved sliced peppers, onions, mushrooms, 1/2 teaspoon salt, and 1/2 teaspoon black pepper. Cook until softened and slightly caramelized, about 12 to 15 minutes. Transfer to a cutting board.

In the same skillet or griddle, heat the remaining 1 tablespoon olive oil over medium-high heat. Add the sliced steak and the remaining 1/2 teaspoon salt and 1/4 teaspoon black pepper. Cook for 1 to 2 minutes without stirring, then stir to finish cooking.

Roughly chop the cooked steak and vegetables on the cutting board and toss together.

Fill each pepper half full with the filling. Place a slice of provolone on top and then fill the pepper completely. Halve the remaining 3 slices of cheese and top each pepper with them. Sprinkle with thyme.

Bake for 15 minutes until the cheese is melted and the peppers are tender. Serve warm.