Melt butter in a large skillet over medium heat. Add onions, mushrooms, green peppers, and pinch of salt. Saute until vegetables begin to soften, 2 to 3 minutes; add minced garlic and cook another minute.
Push vegetables to one side of skillet. Add the sliced meat to the open area and saute until no longer pink, 2 to 3 minutes.
In a separate saucepan, heat Ragu(R) Old World Style(R) Traditional Sauce, Italian seasoning, and crushed red pepper over medium heat.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Slice rolls lengthwise and place, opened, on a baking sheet. Toast for 30 seconds under a broiler on low heat, watching them carefully so they don't burn; remove from oven. Rub toasted sides of rolls with cut side of whole garlic clove; brush lightly with olive oil.
Fold cheese slices into meat and onion/pepper mix and stir until cheese begins to melt; distribute among the toasted roll bottoms. Top with a generous spoonful of Ragu(R) sauce; save the rest for dipping if desired.