Melt the butter and olive oil in a large skillet over medium heat. Add the onion and season with kosher salt and pepper, stir. Add the cloves and allspice and cook until the onions caramelize. Add the mushrooms, 2 cloves minced garlic, bay leaves, and cook for 5 minutes. Add the olives and reduce heat to low.
Trim fat from chicken breasts if desired and cut into cubes. Season with kosher salt and pepper. Put flour on a plate and coat chicken pieces. In a medium-sized skillet, sauté chicken on high for 5 minutes, until well browned. Remove chicken from skillet and drain on paper towels. Return the skillet to high heat and add ½ cup of the white wine. Deglaze the skillet, scraping off all the bits of chicken. Pour this into the skillet with the vegetables, along with the chicken.
Reduce heat to medium and add the other ½ cup white wine, milk, and chicken bouillon. Stir.
Add the other 1 tbsp. olive oil, the other 2 sliced cloves of garlic. Cook for 45 seconds without letting the garlic brown. Add the cans of tomatoes, the oregano, basil, and thyme. Crush the tomatoes with the stirring spoon. Add the tomato paste, ketchup, red wine vinegar, and Worcestershire sauce. Stir.
Simmer uncovered on low while preparing the pasta.
Fill a large saucepan with water and season heavily with kosher salt. Bring to a boil and add the spaghetti. Cook the spaghetti until just under al dente, about 5-6 minutes. Drain the pasta and return it to the saucepan. Reduce the heat to low. Add the sauce to the pasta and finish cooking the spaghetti in the sauce, about 2-3 minutes. Add Parmesan cheese, toss to combine.