Preheat the oven to 400°F (200°C).
Drain the sun-dried tomatoes and press them between paper towels to remove excess oil, then dice them.
Cook the gnocchi in a pot of boiling water according to package directions (about 3–5 minutes), then drain and set aside.
In a large oven-safe skillet over medium-low heat, warm 1 teaspoon olive oil. Add the diced sun-dried tomatoes and minced garlic, season with a pinch of salt and pepper, and cook 2–3 minutes until softened.
In a shaker cup or jar, combine 1 tablespoon flour with 1½ cups stock and shake until smooth. Pour the slurry into the skillet while stirring constantly and cook a few minutes until slightly thickened.
Stir in 2/3 cup cream and 1/2 cup grated Parmesan until combined. Add the cooked gnocchi and toss to coat evenly.
Top the gnocchi with the torn fresh mozzarella pieces, then transfer the skillet to the preheated oven and bake 20–25 minutes until bubbly and the cheese is melted.
Remove from the oven and garnish with fresh basil, extra Parmesan, and crushed red pepper flakes before serving.