Heat the oven to 400°F. Brush pepper halves with 1 teaspoon oil, place cut-side up in a 9-by-13-inch baking dish and bake for 15 minutes.
While the peppers bake, heat remaining oil in a skillet and cook mushrooms and onion for 8 to 10 minutes until their water evaporates and the edges brown.
Add beef and cook for 7 to 8 minutes until finely crumbled and at 160°F. Spoon off excess fat.
Whisk broth, Worcestershire and cornstarch, then stir into the skillet with salt and pepper. Simmer for 2 minutes until lightly thickened and divide the hot filling among the peppers.
Lay half a provolone slice over each pepper half and bake for 12 to 15 minutes until the peppers are tender and the filling reaches 165°F. Rest for 5 minutes before serving.