Preheat the oven to 350 F. Combine the onion, green pepper, jalapeño, mayonnaise, tuna, parsley, red wine vinegar, and Dijon mustard in a medium size bowl. Add salt and pepper to taste.
Gently toss mushrooms in a bowl with olive oil to coat. Lay the mushrooms on a rimmed baking sheet (the hole where the stem had been attached should be facing up) and stuff with the tuna mixture.
Top each mushroom with one slice of tomato and a piece (or two) of cheese.
Bake at 350 F for 20-25 minutes, or until cheese is melted and mushrooms are browned.