Heat 2 teaspoons of olive oil in a large skillet over high heat. Once the oil is shimmering, add the diced or thinly sliced beef. Sprinkle with salt and pepper, and cook until the meat is browned and fully cooked, stirring occasionally to prevent sticking. Transfer the cooked beef to a plate and cover it to keep warm.
While the beef rests, use the same skillet to prepare the veggies. Add the remaining teaspoon of olive oil, followed by the diced onions, red and green bell peppers, and mushrooms. Sauté over medium-high heat until they soften and develop a bit of caramelization, which should take about 5 minutes. Stir occasionally to ensure even cooking.
Return the cooked beef to the skillet and mix it with the sautéed veggies. Add minced garlic and stir for another minute, allowing the flavors to meld. Remove the mixture from heat.
Lay the tortillas flat and spread a thin layer of mayonnaise on one side if you’re using it. Spoon half of the filling onto one side of each tortilla, then layer provolone cheese slices on top. Carefully fold the tortilla over to create a half-moon shape.
Clean your skillet or use a non-stick pan. Heat it over medium heat and lightly grease with a bit of oil or butter if you want extra crispiness. Place the folded quesadillas in the skillet and cook until the tortillas turn golden brown and crispy, about 2-3 minutes per side. Flip once to ensure even cooking and to allow the cheese to melt completely.
Once toasted, transfer the quesadillas to a cutting board. Using a sharp knife or pizza cutter, slice them into triangles. Serve hot and enjoy!