Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add gnocchi; cook, stirring often, until plumped and starting to brown, 5 to 7 minutes. Transfer to a bowl.
Heat remaining 1 teaspoon oil in the skillet. Add onion; cook and stir over medium heat for 2 minutes. Stir in water and garlic, cover, and cook until onion is soft, 4 to 6 minutes. Add chard; cook and stir until starting to wilt, 1 to 2 minutes. Stir in tomatoes, beans, and black pepper; bring to a simmer. Stir in gnocchi; sprinkle with mozzarella cheese and Parmesan cheese. Cover and cook until cheeses are melted and sauce is bubbling, about 3 minutes.
