Cook the linguine according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.

In a large bowl, combine ground beef, Parmesan cheese, breadcrumbs, egg, minced garlic, Italian seasoning, salt, and pepper. Mix until just combined. Form the mixture into meatballs, about 1 inch in diameter.

In a large skillet over medium heat, melt 2 tablespoons of butter. Add the meatballs and cook for about 8-10 minutes, turning occasionally, until browned and cooked through. Remove the meatballs from the skillet and set aside.

In the same skillet, add the remaining 2 tablespoons of butter and chicken broth. Stir in red pepper flakes if using. Bring to a simmer, scraping up any browned bits from the bottom of the pan.

Add the cooked linguine to the skillet, tossing to coat in the garlic butter sauce. If the pasta seems dry, add reserved pasta water a little at a time until desired consistency is reached.

Return the meatballs to the skillet and gently toss to combine.

Serve immediately, garnished with chopped parsley and additional Parmesan cheese if desired.