Heat a large skillet with 1/2 tablespoon olive oil over medium-high heat. Once hot, add the ground beef. Season with the 1 teaspoon salt and 1/2 teaspoon black pepper. Brown both sides completely for 3-4 minutes each before breaking apart and fully cooking. Transfer the cooked beef to a bowl and set aside.
Add the remaining 1 tablespoon olive oil, followed by the mushrooms, onion, and bell pepper. Season with remaining 1 teaspoon salt. Cook for 4-5 minutes until the veggies have softened before adding the beef back to the skillet. Salt and pepper to taste.*
Turn off the heat and add the cheese to the top of the skillet. Cover to melt with the residual heat.
Serve on a toasted roll with light mayo and sliced peppers, over fries, in sliders or quesadillas, or whatever else you can come up with.