Preheat your oven to 350°F if you plan to top the pasta with provolone cheese.
Cook the pasta in a large pot of salted water until just al dente. Reserve 1/2 cup of pasta water before draining. Drain the pasta and toss it with a small amount of olive oil, then set aside.
In a large pot or Dutch oven, heat 1 tablespoon of olive oil over medium-high heat. Add the ground beef and cook, breaking it apart as it cooks, until it's almost fully browned. Season with 1/2 teaspoon of salt and 1/4 teaspoon of pepper, then continue cooking until the beef is thoroughly browned. Transfer the cooked beef to a plate, leaving the drippings in the pot.
Add the remaining 2 tablespoons of olive oil to the pot and heat over medium-high. Add the diced onion and sauté for about 5 minutes. Then, add the chopped bell peppers and cook for another 3 minutes, or until the onions have softened. Stir in the minced garlic and red pepper flakes, cooking for 30 seconds until fragrant.
Sprinkle the flour into the pot and cook for 1 minute, stirring constantly. Lower the heat to low, and gradually whisk in the beef broth, followed by the half-and-half. Mix in the Worcestershire sauce, balsamic vinegar, Dijon mustard, beef bouillon, and the dried herbs and spices. Season with 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Increase the heat to medium-high and bring the sauce to a simmer, stirring frequently until it thickens slightly.
Reduce the heat to low and slowly add the torn provolone cheese, stirring until melted. Then, stir in the shredded cheddar cheese until fully melted and combined with the sauce.
Add the cooked ground beef back to the pot, followed by the pasta. If the sauce seems too thick, gradually add some of the reserved pasta water to reach your desired consistency. Taste the pasta and adjust the seasoning with additional salt and pepper if needed.
For an optional cheesy finish, top the pasta with the remaining provolone slices. Cover the pot and bake in the preheated oven for 5-10 minutes until the cheese has melted. Garnish with parsley if desired, and enjoy your meal!