Add the flour, salt, and pepper to a gallon-size food storage bag. Mix together in the bag.
Add the chicken breasts to the bag, seal, and shake to coat the chicken in the flour mixture.
To a large skillet, add 2 tablespoons of olive oil and place over medium heat. Brown the chicken breasts, cooking for 4-5 minutes per side (add more oil as needed). Transfer to a plate and set aside once browned. (The chicken will finish cooking later.)
Reduce the heat to medium-low and add 1 tablespoon of olive oil to the same skillet. Once the oil is hot, add the onions and garlic and cook for about 5 minutes stirring frequently to prevent the garlic from burning.
Add the chicken broth, sun-dried tomatoes, red pepper flakes, oregano, and thyme to the skillet. Scrape up any brown bits on the bottom of the pan into the sauce.
Stir in the heavy cream and parmesan cheese and bring the sauce to simmer.
Then add chicken breasts back to the sauce and cook for another 8-10 minutes or until the chicken is cooked through (165 degrees F internal temperature). You want the sauce at a low simmer to allow it to thicken. The coating from the chicken will help thicken the sauce too.
Serve the chicken with some of the sauce over cooked spaghetti (or your favorite pasta) and garnish with basil, parmesan, and a pinch of red pepper flakes. Serve warm.
Notes
Nutritional information is for 1 chicken breast and 1/4 of the sauce. It does not include any side dishes.
You can use more sun-dried tomatoes to taste as desired.
Half-n-half or whole milk can be substituted for heavy cream, but the sauce will have a slightly different taste/texture.