In a food processor, combine the sun-dried tomatoes, fresh basil, Parmesan cheese, garlic, and pine nuts. Pulse the mixture until finely chopped. With the processor running, slowly drizzle in the olive oil until the pesto reaches a smooth consistency. Taste and season with salt and freshly ground black pepper as needed. Set aside. You'll use some in the meatballs and some in the sauce.
In a large bowl, combine the ground beef, breadcrumbs, Parmesan cheese, egg, 2 tablespoons of the sun-dried tomato pesto, chopped onion, minced garlic, oregano, salt, and pepper. Use your hands to gently mix until just combined. Avoid overmixing to keep the meatballs tender. Roll the mixture into meatballs about 1 to 1.5 inches in diameter, making approximately 20–24 meatballs.
Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the meatballs in batches to avoid overcrowding. Cook, turning occasionally, until browned on all sides and cooked through, about 8–10 minutes. Remove the meatballs from the skillet and set aside on a plate.
In the same skillet, add 1 tablespoon olive oil if needed. Sauté the chopped onion over medium heat until translucent, about 3–4 minutes. Add the minced garlic and cook for an additional minute until fragrant. Stir in ½ cup of the sun-dried tomato pesto and cook for 1–2 minutes to meld the flavors. Pour in the heavy cream and chicken or vegetable broth, stirring to combine. Bring the mixture to a gentle simmer.
Stir in the grated Parmesan cheese until melted and the sauce is smooth. Taste and adjust seasoning with salt and pepper as needed.
Carefully add the cooked meatballs back into the skillet with the sauce. Spoon the sauce over the meatballs to coat them. Let the meatballs simmer in the sauce for 5–7 minutes to absorb the flavors and ensure they are fully heated through.
Garnish with fresh basil leaves if desired. Serve hot over pasta, rice, mashed potatoes, or with crusty bread to soak up the delicious sauce.