Preheat the oven to 400°F.

Prepare the peppers by slicing about a third off the top and removing the ribs and seeds, leaving the stems on.

Slice the pepper lids into thin strips.

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

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

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

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

Remove the peppers from the oven and carefully fill each with the steak and vegetable mixture. Place a slice of provolone on top and fill each pepper completely. Halve the remaining 3 slices of cheese and place on top. Sprinkle with thyme.

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