Mushroom and Sweet Onion Cheesesteak

I found this recipe on cooking light and tried it this week. I absolutely loved it but forgot to melt the cheese on top. It tastes better when you do.

2 teaspoons olive oil, divided
12 ounces top round steak, cut into thin strips
1 1/2 cups thinly vertically sliced Vidalia or other sweet onion
1 teaspoon bottled minced garlic
1 (8-ounce) package presliced mushrooms
1/4 cup Madeira wine (I used chicken broth)
1/2 cup green bell pepper strips
1/2 cup red bell pepper strips
1 teaspoon Worcestershire sauce
1/4 teaspoon salt
1/4 teaspoon black pepper
1 cup (4 ounces) shredded reduced-fat cheddar cheese
4 (2-ounce) ciabatta rolls

Heat a large nonstick skillet over medium-high heat. Add 1 teaspoon oil to pan; swirl to coat. Add steak to pan; cook 2 minutes or until browned, turning occasionally. Remove steak from pan. Add remaining 1 teaspoon oil to pan; swirl to coat. Add onion and garlic to pan; sauté 1 minute, stirring occasionally. Add mushrooms; sauté 6 minutes. Stir in wine; cook until liquid evaporates (about 1 minute). Add bell peppers; sauté 4 minutes. Return steak to pan. Stir in Worcestershire, salt, and black pepper; cook 1 minute or until thoroughly heated. Remove from heat. Sprinkle mixture with cheese; stir until cheese melts. Divide mixture evenly among rolls.