Cook chicken. In a 12-inch skillet, heat 2 tablespoons of oil on medium-high heat. While the oil heats, season chicken with salt and pepper on both sides. Sear chicken, cooking on each side for 2-3 minutes. Set aside on a plate.
Saute mushrooms. Reduce heat to medium-low. Add an additional tablespoon or more of oil if needed, and add mushrooms to the pan. Cook for about 5 minutes until browned and set aside on a plate & refrigerate for later.
Cook garlic and onion. Add a tablespoon or more of oil and add the chopped onion, cooking 3-5 minutes until onions are translucent. Add garlic and cook for an additional minute.
Put veggies and seasoning in the slow cooker. Put the onions and garlic mixture in the slow cooker. Add crushed tomatoes. Add the whole tomatoes, crushing tomatoes with your hand when placing them in the slow cooker. Add carrots, thyme, 1 teaspoon salt, and ½ teaspoon pepper and stir together.
Add broth and base. Measure broth in a measuring cup. Add chicken base to the measuring cup and whisk together. Pour into the slow cooker, scraping all of the bouillon base out with a spatula into the tomato mixture, and stir to combine.
Add chicken and cook. Place the chicken into the tomato mixture and nestle into the slow cooker so that the chicken is covered with the sauce. Cook on high for 2 hours.
Add mushrooms. At two hours, add in the fresh rosemary, roasted red peppers, cooked mushrooms, capers, and Kalamata olives if using. Cook for an additional 15-30 minutes. Check the chicken with a meat thermometer to see if the internal temperature is 165℉ and remove the chicken to a plate.
Thicken. Remove the lid from the slow cooker and continue to cook the sauce until it has thickened, an additional 30-45 minutes.
Cook pasta. While the sauce thickens, bring water to a boil and cook spaghetti according to package directions, or prepare other pasta or food to serve with chicken. Drain and transfer noodles to a serving platter or individual plates.
Season and serve. Taste the sauce and add additional salt and pepper if desired. Return chicken to the sauce. Place chicken onto pasta, adding additional sauce to serve, and garnish with parsley and parmesan cheese.