In a large bowl, using a rubber spatula, combine egg, garlic, chicken, pork, bread crumbs, red pepper flakes, ½ cup Parmesan, half of thyme, and 1 teaspoon salt until combined.
Portion meat mixture into balls about 1 tablespoon each and arrange on a parchment-lined baking sheet. Freeze 5 minutes.
In a large nonstick skillet over medium heat, heat 2 tablespoons tomato oil. Add meatballs and cook, turning occasionally, until browned on all sides, 6 to 7 minutes. Transfer meatballs to a plate.
In same skillet over medium-high heat, heat remaining 1 tablespoon tomato oil. Add onion and sun-dried tomatoes; season with salt. Cook, stirring occasionally, until onion is softened, about 7 minutes. Add remaining thyme and cook, stirring, until warmed through, about 1 minute more. Stir in broth, then cream. Bring to a simmer and cook, stirring occasionally, until slightly thickened, 3 to 4 minutes. Return meatballs to skillet and toss in sauce to coat. Stir in remaining ¼ cup Parmesan. Top with basil.
