Place a large saucepan of water on a burner, add salt and turn the heat to HIGH so that it comes to a boil for the gnocchi.
Place the cherry tomatoes in a large nonstick skillet. Drizzle with the olive oil and season with salt and black pepper to taste. Turn the heat up to medium-high.
When it's hot, place a lid over the skillet and let the tomatoes fry, pop and burst for 2-3 minutes. Stir, then place the lid back on and repeat for another 3-4 minutes.
At this point, the saucepan of water should be boiling. Add the gnocchi and cook according to the package directions then drain and keep warm.
Add the wine, garlic and red pepper flakes. Boil for 2-3 minutes to reduce the wine.
Add the anchovy paste, olives, capers and heat through.
Add the parsley, basil, sugar and salt if needed. Toss the gnocchi into the sauce and stir. Serve in bowls with freshly grated Parmesan cheese.