Heat the olive oil in a skillet over medium heat.
Add the minced garlic and cook briefly until fragrant.
Add the chopped or sliced steak to the skillet.
Season with salt and black pepper to taste.
Cook the steak until fully cooked and lightly browned.
Remove the steak from the skillet and set aside.
Keep the steak warm while preparing the vegetables.
In the same skillet, add the sliced green pepper, red pepper, onion, and chopped mushrooms.
Add a small amount of additional oil if needed.
Sauté the vegetables until tender and lightly browned.
Return the cooked steak to the skillet.
Stir until the steak and vegetables are evenly combined.
If using mayonnaise, spread 1 tsp over each tortilla.
Divide the steak and vegetable filling evenly between the tortillas.
Place the Provolone cheese halves over the filling.
Fold each tortilla over to enclose the filling.
Heat a clean skillet over medium heat.
Add a very small amount of oil to the skillet.
Place one folded tortilla in the skillet.
Cook until the bottom is golden brown and crisp.
Carefully turn the quesadilla over.
Cook the second side until golden brown and the cheese is melted.
Repeat the process with the second tortilla.
Transfer the quesadillas to a cutting board.
Let them rest briefly before slicing.
Slice into wedges and serve warm.