Add sliced peppers, onions, and mushrooms to a large skillet with the olive oil, salt, and pepper, and saute over medium heat until veggies are soft, about 20-25 minutes.
While veggies are cooking, preheat oven to 350. Slice the sub rolls in half and place them on a baking sheet. Spread each with 2 tsp dijon mustard and 1 tbsp mayo*.
When the veggies are soft, evenly divide among the four rolls and top with 1/4 cup Italian dressing and one slice each of cheddar and provolone cheese.
Bake open faced for about 5 minutes, or until the cheese it melted and the bread is toasted. Put the top on the sub and serve hot.
* Adjust mustard and mayo according to taste. I tend to like a little more mustard but some people find it too strong.