Gather and prepare your ingredients, including mincing the onion, carrots, celery, and garlic, and chopping the fresh basil.
In a Dutch oven or a large, heavy-bottomed pot, heat 1 tablespoon of olive oil over medium-high heat.
Add the onions, carrots, celery, and garlic to the pot and sauté, stirring occasionally, until softened, around 6 minutes.
Add the ground beef chuck, lean ground sirloin, and red pepper flakes (if using) to the pot. Break up the ground meats using a wooden spoon to ensure even cooking. Continue cooking the ground meat until browned and cooked through on medium-high heat. Drain any excess grease if necessary. Remove the casings from the Italian pork sausages and add them to the pot. Break the sausages apart using your wooden spoon, mixing them in with the cooked ground meat. Stir in the 3 tablespoons of tomato paste, combining it with the meat and vegetables in the pot. Cook for an additional 5 minutes to let the flavors meld together. Bring a large pot of water to a boil and add a generous pinch of salt. Add the pound of orecchiette and cook according to the package instructions until al dente. Drain the pasta, reserving 1 cup of pasta water for adjusting the sauce's consistency, if necessary.
Stir in the fresh basil and season the sauce with salt and pepper to taste.
Add cooked orecchiette to the bolognese sauce and mix gently to combine. If needed, add a small amount of the reserved pasta water to reach the desired consistency. Serve your Orecchiette Bolognese with a sprinkling of freshly grated Parmesan cheese on top, if desired.