Drizzle the olive oil and add the butter to a deep skillet or pot over medium to medium-high heat then add the bite size chicken pieces to the hot skillet.
Season with salt and pepper to taste then leave the chicken in place without moving for 2 minutes letting the chicken sear. Turn the pieces over and continue until they’re cooked through and remove from the skillet.
In the same skillet (don't wash it!) reduce the heat to low then add the grated garlic, chicken stock, milk, heavy cream, 1 teaspoon of salt and the dry (uncooked) pasta.
Cover, bring to a boil then reduce the heat and simmer with a light boil for 10-14 minutes or until the pasta is al dente. Stir occasionally so the pasta doesn't stick to the bottom of the pan.
Return the chicken to the pot, fold in the chopped parsley then stir. Taste and adjust salt as needed then serve right away with extra parmesan cheese at the table.