Preheat grill to medium-high or preheat the broiler. Combine Cheddar and Gruyere in a small bowl. Gently mix beef, Worcestershire, paprika and pepper in a large bowl, preferably with your hands, without overworking. Shape into 8 thin, 4-inch-wide patties. Mound 2 tablespoons of the cheese mixture on each of 4 patties, leaving a 1/2-inch border. Cover each with one of the remaining patties. Crimp and seal the edges closed.
To grill: Lightly oil the grill rack. Grill the stuffed patties over medium-high heat, about 4 minutes per side for medium-well. (Be sure not to press the burgers as they cook or they'll split open and the cheese will ooze out.)
To broil: Cover a broiler pan with aluminum foil and coat with cooking spray. Broil the stuffed patties in the upper third of the oven, about 4 minutes per side for medium-well. In either case, let the burgers stand for 5 minutes before serving. Serve with your favorite toppings and dressing.
Cook's Note: Use any mixture of hard or semi-hard cheeses, Swiss and Gouda OR Asiago and Parmigiano-Reggiano pair well.