Preheat the oven to 400°F (200°C).
Drain the sun-dried tomatoes and press them between paper towels to remove excess oil; dice and set aside.
Cook the gnocchi according to the package directions (about 3–5 minutes), drain, and set aside.
Heat 1 teaspoon olive oil in a large oven-safe skillet over medium-low heat. Add the diced sun-dried tomatoes and minced garlic, season with a pinch of kosher salt and black pepper, and cook 2–3 minutes until softened.
In a shaker cup or small jar, combine 1 1/2 cups stock and 1 tablespoon flour; shake until smooth to make a slurry. Pour the slurry into the skillet while stirring constantly and cook a few minutes until it warms and begins to thicken.
Stir in 2/3 cup cream and 1/2 cup grated Parmesan until combined. Add the cooked gnocchi and stir gently to coat.
Top the gnocchi mixture with torn or sliced mozzarella, 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 top with fresh basil, extra Parmesan, and crushed red pepper flakes before serving.