Combine all the ingredients for the marinade in a large glass measuring cup or mixing bowl and stir vigorously until well combined.
Place the chicken thighs in a single layer in a non-reactive container such as a glass or porcelain baking dish and pour in the marinade; toss the chicken thighs around until they are completely coated. Make sure that the marinade makes it all the way to the bottom of the dish. Cover with a piece of plastic film and place in the refrigerator to marinate for at least 4 hours, but preferably overnight.
Heat a few tablespoons of olive oil (or any other healthy cooking oil) in a large skillet or saute pan set over high heat. When the pan is nice and hot, add half the pieces of chicken, nice-looking side down, and cook them without moving them for about 4 minutes, until they turn opaque about half way up and develop a nice golden crust. Flip the pieces of chicken and cook them for another 3 to 4 minutes, until the meat is cooked all the way through and the juices run clear. Remove to a plate and repeat with the remaining pieces of chicken.
Return the reserved chicken to the skillet, add the chicken stock and white wine (as well as any marinade potentially left behind, for even more flavor) and simmer for about 5 minutes, scraping the bottom of the pan gently to detach all the bits and pieces that stuck to it.
Combine the heavy cream (or whole milk) with the cornstarch and water in a glass measuring cup and whisk until well combined. Add that to the skillet and simmer, stirring gently, until the sauce is fully thickened, about 1 minute.
Delicately stir in the cheese, olives and sun-dried tomatoes. Kill the heat and add the cherry tomatoes and fresh parsley.
Serve immediately over your choice of cooked pasta, noodles, rice or even cauli-rice.