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In a large skillet over medium heat, heat 1 Tbsp. oil. Add tomatoes and cook, stirring occasionally, until just starting to brown, 2 to 3 minutes. Add garlic, thyme, and red pepper flakes and cook, stirring, until fragrant, 1 to 2 minutes more.
Push tomato mixture to edges of skillet and pour remaining 1 Tbsp. oil into the center. Add gnocchi and toss to coat in oil. Cook, undisturbed, 2 minutes, then stir in broth and cream to combine with tomato mixture. Bring to a simmer and cook, stirring occasionally, until gnocchi is tender and sauce is slightly reduced, 4 to 5 minutes.
Stir in Parmesan. Top with basil.