Preheat the oven to 400°F.

Place a pepper on a cutting board so it is laying on its side. Use a knife to slice about a third off the top, from stem to end. Repeat with all other peppers. Use your hands to remove the ribs and seeds inside the pepper and discard them. Leave the stems on.

Slice the pepper 'lids' into thin strips. You will cook these with the onions and mushrooms.

Place the peppers on a baking dish cut side-up 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, ½ teaspoon salt, and ½ teaspoon black pepper. Cook, stirring occasionally, until they softened and start to caramelize around the edges, 12 to 15 minutes.

In the same skillet or griddle over medium-high heat, heat the remaining 1 tablespoon olive oil. Add the sliced steak and the remaining ½ teaspoon salt and ¼ teaspoon black pepper. Cook for 1 to 2 minutes without stirring.

Transfer the cooked steak onto the cutting board. Use a chef’s knife to roughly chop the steak and the vegetables into small pieces. Toss them together with your hands to combine.

Remove the peppers from oven. When they are cool enough to handle, carefully fill each pepper half full with the filling. Place a slice of provolone on top of the filling. Top with more filling until the pepper is full.

Halve the remaining 3 slices of cheese and top each pepper with them. Sprinkle the tops with thyme.

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