Grease a skillet with cooking spray and set over medium heat. Break up sandwich steaks by hand and add to the skillet; cook and stir until golden brown, 5 to 7 minutes. Drain excess grease. Stir in onion, Worcestershire sauce, garlic, salt, and pepper.
Unroll pizza dough onto a flat work surface; stretch into a 12-inch square. Spread a thin layer of beef mixture on one end, leaving a 1-inch border on the sides. Tear 4 slices of American cheese in half and lay on top. Roll up the dough, pinching the sides together. Repeat layering and rolling until all the beef mixture and cheese is used up.
Seal the top of the roll; transfer to an ungreased baking sheet.
Bake in the preheated oven until top is golden brown, 12 to 15 minutes. Let stand for 5 minutes before cutting into 1-inch slices.