Heat olive oil in a 9-inch ovenproof skillet over medium-high setting. When hot, carefully pour in the tomato-egg mixture and cook without stirring. When sides of frittata begin to set (after about 5 minutes), place skillet in oven. Bake until eggs in center barely set, about 15 minutes. Let frittata cool in skillet for 5 minutes, then run a knife around its perimeter. Set an ovenproof plate on top of skillet (the plate’s underside should face up) and, holding plate to skillet with both hands, gently flip over. Lift off skillet and set aside.
Combine tomato paste and cheese in a bowl. Using a spatula, evenly spread mixture on top of frittata. Return to oven and bake until cheese melts and slightly bubbles, 7 to 10 minutes more. Slice into wedges and serve.