In skillet, heat oil and brown beef, seasoning with salt and pepper.
Once browned, remove beef leaving liquid in pan. Add chopped onions and mushrooms to cook, adding butter to help cook down.
Seasoning with Worcestershire, ketchup, and stock and stir well. Place lid on and turn heat on low.
Slice peppers in half lengthwise and remove seeds (if heat is preferred, leave a few seeds in!). Lay in baking sheet and line with half of the provolone.
Carefully fill each pepper with the beef mixture, pressing into the pepper. Top with more provolone.
Bake at 350 for about 30 minutes, or until cheese starts to become golden.
While baking, in skillet, warm olive oil and butter. Add stock and bring to a soft simmer.
Add in cream until also simmering. Sprinkle in both Italian and provolone cheese and stir well to melt.
Turn heat low and continue to stir until thickened.
Serve peppers drizzled with provolone sauce. Enjoy!