Heat 1/2 of oil and butter in a large nonstick skillet over medium-high heat. Add Portobello mushrooms and cook 2-3 minutes per side, until nicely browned. Remove to a plate.
Add remaining oil and butter and sauté the onion and pepper until softened and beginning to brown, about 5 minutes.
Add mushrooms back to pan and add soy sauce, Worcestershire sauce, and thyme. Cook for another minute or two. Remove from heat and season with salt and pepper.
Divide mushroom mixture between sub rolls. Top each roll with 1 or 2 slices of cheese. Place on a baking sheet and broil until cheese melts and bread is lightly toasted.