Heat 1 tablespoon oil in a large skillet over medium-high; cook beef about 6-8 minutes until browned and cooked through, breaking it apart. Season with salt, pepper, and Worcestershire; remove to plate.
Add remaining oil to skillet; sauté peppers, onions, and mushrooms about 8-10 minutes until softened and starting to caramelize.
Add garlic; cook 1 minute until fragrant. Return beef; stir together.
Divide rice among 4 bowls.
Top with beef and vegetables, then 2 provolone slices per bowl over hot mixture.
Stand 1-2 minutes to melt cheese; serve immediately.