Preheat oven to 400 degrees.

In a large skillet, heat oil over medium heat . Add mushrooms and garlic; saute for 2 minutes. Add beef tips; cook until beef has lost its redness. Add caramelized onions, Worcestershire sauce, and hot sauce; cook until onions are heated through. Season with salt and pepper.

Split rolls and arrange halves on a baking sheet. Toast in oven until rolls are lightly browned; remove from oven.

Spoon beef mixture onto bottom half of each roll; top with Parmesan-Romano cheese blend. Return bottom halves of rolls to oven until cheese has melted.

Replace top halves of rolls and serve.

Peel and quarter onions. Slice vertically or horizontally (whichever you prefer) into 1/4-inch pieces. You should have enough onions to generously fill a 5-quart saute pan.

In an empty saute pan, melt butter over medium heat on stovetop; add oil and heat until fat is hot. Add onions and cook, stirring constantly, until onions are just beginning to brown (approximately 10 minutes). Reduce heat to medium low and continue to cook and stir until onions reach a light caramel color (20 to 35 minutes).

Let onions cool, then store in an airtight container in the refrigerator for up to one week.