Place edamame, corn, onion, garlic, olive oil, salt and pepper into a 13 x 9 pan and stir to combine. Place on middle rack of the oven and roast for 10 to 15 minutes, just until the edamame begins to brown.
Remove from oven and place in refrigerator until completely cool, approximately 30 minutes.
Add tomato, basil and vinegar to mixture and toss to combine. Taste; adjust seasoning as needed. Serve chilled or at room temperature.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add gnocchi and cook, stirring often, until it is plumped and starting to brown; about 5-7 minutes. Place cooked gnocchi in a large bowl.
Add 1 teaspoon of oil and onion to the pan and cook for 2 minutes. Stir in garlic and water. Cook until onion is cooked.
Add spinach and cook by stirring until spinach begins to wilt
Stir in tomatoes, beans, and simmer. Add gnocchi and sprinkle with both cheeses.
Cook until cheese is melted and sauce is bubbling; about 3 minutes.