Heat olive oil on medium-high heat, add sliced mushrooms and garlic - and cook the vegetables for about 3 minutes. Add diced sun-dried tomatoes. Reduce heat.
Dissolve 2 cubes of chicken bullion in 2 cups of boiling water. Carefully add the broth to the skillet - continue to cook the vegetables in a chicken broth on medium heat until the mushrooms and sun-dried tomatoes absorb some of the broth and the broth reduces somewhat. Add half and half, heavy cream and bring to boil just for a short moment. Add Parmesan cheese and cook the sauce, stirring, for a couple of minutes, on low-medium heat until the cheese melts. Add the basil.
If your sauce is too thick at this point - add another ½ cup half and half. If your sauce looks thin to you - do not continue simmering the sauce to thicken it as you will be adding pasta shortly (in the next step) - and pasta will absorb some of the sauce liquid. Even if the sauce looks thin now, it will not be so thin once you add pasta.
Cook fettuccine al dente according to the package instruction. Drain and rinse in cold water (this will stop the cooking). Add the fettuccine into the sauce and continue cooking the sauce with the pasta in it, on medium heat, for a couple of minutes (or more - to achieve the desired thickness) stirring constantly to coat well.
Note: do not add salt to the creamy sauce because it should already be salty enough from the dissolved chicken cubes. Only in the very end when the sauce is done, you may add some salt if needed.
How to cook chicken breasts on stove top:
Pound the chicken breasts to an even thickness. If you don't have the right equipment to pound a chicken, wrap the chicken breast in plastic, and use a heavy pan to pound it until you reach the desired thickness. Don't overdo it. While this step is desirable to achieve even cooking, you can also skip it. :)
Season both sides of chicken breasts with salt and pepper. You can also add a touch of Cajun spice on both sides, if desired.
Heat the large pan over medium-high heat. When the pan is hot, add olive oil and swirl it around the pan. Immediately, add the chicken breasts and cook them for 2 minutes on one side.
Flip each chicken breast over to the other side, cover, and cook for 2 more minutes on the other side.
Flip them over again to the other side, turn off the heat, cover the pan with the lid and let the chicken breasts sit covered for about 10-15 minutes (depending on the thickness of chicken breasts). If your chicken breasts are very thick, you might even need 20 minutes. After 10-15 minutes are over, make a thin incision in the center of one of the chicken breasts to check for doneness and to make sure there is no pink in the middle.
How to serve:
Place ¼th of pasta from the pan on each of 4 dinner plates. Top the pasta with grated Parmesan cheese. Then, top each pasta with a chicken breast. I love to serve pasta with salt and pepper mills, so that people can add freshly ground pepper or more salt to their dish.
What is half and half? To make 1 cup of half and half, combine ½ cup of milk and ½ cup of cream.