Heat 1 tablespoon olive oil in a large skillet over medium heat. Add sun-dried tomatoes and cook for 2–3 minutes until slightly browned.
Stir in garlic, thyme, and red pepper flakes. Cook for another 1–2 minutes until fragrant.
Push the mixture to the sides and add remaining oil to the center. Add gnocchi and toss to coat. Let cook undisturbed for 2 minutes.
Pour in broth and cream, stirring everything together. Simmer for 4–5 minutes until the gnocchi is tender and the sauce thickens.
Stir in Parmesan until melted and creamy.
Finish with fresh basil and serve warm.