Arrange a rack 6 to 8 inches below the broiling element and set the oven to broil.
Heat 1 tablespoon of the olive oil in a 12-inch cast-iron or other broiler-safe, heavy-bottomed skillet over medium heat until shimmering. Break up 1 (16- to 18-ounce) package of the potato gnocchi into individual gnocchi and add to the skillet in a single layer. Cook, tossing occasionally, until the bottoms are golden-brown, 5 to 7 minutes. Transfer to a plate, and repeat with the remaining 1 tablespoon olive oil and 1 package gnocchi.
Return all gnocchi to the skillet. Stir in 1 (about 24-ounce) jar marinara sauce and bring to a simmer. Sprinkle evenly with 5 ounces shredded mozzarella cheese.
Transfer the skillet to the oven and broil until the cheese is melted, bubbly, and browned in spots, 1 to 2 minutes. Garnish with the torn fresh basil leaves and/or red pepper flakes if desired.
