Put a small saucepan (about 7 inches, 2 quarts) over a medium flame and add the oil, garlic and mint all together and saute for 2-3 minutes until the garlic just begins to color. Add the tomatoes and water stirring occasionally until the sauce comes to a boil. Lower the flame to low and simmer for 8-10 minutes.
Remove from heat and set aside.
For the stuffing:
Remove the stems from the mushrooms and chop them into a 1/4 inch dice.
In a 12 inch skillet add the oil and onions together and saute over a medium flame until translucent. About 4-6 minutes. Add the stems and a pinch of salt and saute for another 2-3 minutes. Set aside and let cool. In the meantime mix the rest of the filling.
In a medium sized mixing bowl combine the pecorino cheese, breadcrumbs, parsley, salt and pepper and mix together.
Once cooled add the mushroom stems and onions to the mixing bowl and mix together until combined.
In the same skillet used for sauteing the stems and onions add a layer of sauce, about 1 1/2 cups.
Fill each mushroom with about 2 tablespoons of filling and place them back into the skillet.
Spoon about 1-2 teaspoons of sauce over each mushroom depending on size and add 1 teaspoon of provolone over the sauce.
Cover the skillet and place it back on the stove over a medium flame until the sauce begins to bubble, about 1-2 minutes. Lower the flame to low and simmer for 10-12 minutes, or until the mushrooms are tender and easily pierced with a fork.