Heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add gnocchi and cook, stirring often, until plumped and starting to brown, 5 to 7 minutes. Transfer to a bowl.
Add the remaining 1 tablespoon oil and onion to the pan and cook, stirring, over medium heat, for 2 minutes. Stir in garlic and water (1/2 cup). Cover and cook until the onion is soft, 4 to 6 minutes. Stir in tomatoes, beans and pepper and bring to a simmer. Stir in the gnocchi and chard and cook, stirring, until starting to wilt, 1 to 2 minutes.
Sprinkle with mozzarella and parmesan. Cover and cook until the cheese is melted and the sauce is bubbling, about 3 minutes. Season with salt and pepper.