Heat the canola oil and butter in a large skillet over medium heat. Clean the Portobello mushrooms by removing the stems and gills, then slice them into 1/2-inch thick slices.
Add the sliced onions and red bell peppers. Sauté for about 5-7 minutes until soft and caramelized.
Add the sliced Portobello mushrooms to the skillet and cook for another 5-7 minutes until tender.
Pour in the soy sauce and Worcestershire sauce, add thyme, and season with salt and pepper. Cook for an additional 2-3 minutes.
Reduce the heat to low and lay the slices of Provolone cheese over the mixture. Cover the skillet to help the cheese melt, about 2-3 minutes.
Slice the sub rolls in half. Spoon the mushroom mixture onto the bottom half of each roll, top with the other half, and serve immediately.
