Make the meatballs
Combine the breadcrumbs and milk in a large bowl and let the crumbs soak up all the milk. Add the beef and pork along with the cheese, garlic, salt, chili flakes, eggs, and egg yolk. Gently mix, being careful not to overwork the meat, then form into about 18 golf ball–sized meatballs. Arrange on a large baking sheet and sprinkle very lightly on both sides with the fine dry breadcrumbs (just a super-light dusting). Chill for 1 hour and up to 24 hours to help the meatballs keep their shape. Heat the oil in a large skillet over medium heat, add the meatballs (working in batches if necessary), and brown on all sides, about 8 minutes total. Transfer the meatballs to a plate and carefully drain all but ¼ cup of the fat and oil from the skillet. Cover the meatballs to keep warm.
Make the sauce
Heat the remaining fat and oil over medium heat. Add the onions and cook, stirring, until softened and translucent, about 10 minutes. Add the garlic and cook for 1 more minute. Stir in the tomato paste and cook until caramelized and absorbed, about 2 minutes. Add the crushed tomatoes, oregano, chili flakes, thyme, parsley, rosemary, salt, sugar, and vinegar. Bring to a boil, reduce the heat to low, and simmer until the sauce thickens, 25–30 minutes.
Finish and serve
Gently nestle the meatballs into the sauce, return to a simmer, and cook until the meatballs are fully cooked through and have absorbed some of the sauce, 20–25 minutes. Season with salt and pepper to taste. While the meatballs simmer, cook the pasta al dente according to package directions. Drain and add to the pot with the meatballs and sauce, or portion individually. Garnish with cheese and basil.