Cook sausage in a large nonstick skillet over medium heat until hot, 4 to 5 minutes. Stir in potatoes.

Whisk eggs, cheese, salt, and black pepper together in a large bowl; pour over sausage mixture in the skillet. Cook over medium-high heat for 2 minutes, occasionally lifting the edge with a spatula and tilting the skillet to allow uncooked egg to flow underneath. Do not stir.

Reduce heat to medium-low; cover the skillet. Cook until eggs are set, 14 to 17 minutes.

Top frittata with tomatoes and green onions. Cut into 8 wedges; serve.