Heat grill to medium-high. In a large bowl, gently fold together beef, Worcestershire sauce, 1 tablespoon salt, and 1 teaspoon pepper. Form into 8 equal-size mounds.
Shape cheese into 8 equal-size disks. Press a small well in the center of each beef mound. Place cheese in well; wrap beef around cheese, pinching to seal.
Lightly oil grates. Place burgers on grill; cover. Cook until grill marks are visible on first side, 4 to 6 minutes. Turn burgers with a spatula; cook until grill marks are visible on other side and meat is just slightly pink in the middle, 4 to 6 minutes more for medium-rare.
To serve, layer bottom roll halves with spinach, burgers, tomato, and mushrooms, if using, dividing evenly. Spread
top roll half with mustard and Roasted Red-Pepper Sauce, as desired.