Heat a skillet with olive oil and sautee the red bell peppers, onions, and mushrooms.
Add the cheese to the vegetables and mix until melted.
Butter one side of each slice of bread and full the sandwiches with the cheese and vegetable mixture. Grill in a pan until the bread is carmelized.
Make the aioli by adding all the ingredients to a blender and blending until smooth.
Open the sandwiches and add the aioli, then serve.