Preheat the oven to 375 degrees F. Pound the chicken breasts between 2 pieces of plastic wrap to about 1/4-inch thickness. In a small bowl, mix together the breadcrumbs, parsley, grated Parmesan, and garlic. Slowly add 1/2 cup olive oil until the mixture becomes the consistency of thick paste. Evenly spread the mixture down the center of each piece of chicken, leaving room around the edges. Roll as tightly as you can and secure with toothpicks or cotton string.
Heat the remaining 1 tablespoon oil in a large ovenproof, nonstick skillet over medium heat. Carefully add the chicken and brown on each side. Transfer the skillet to the oven and bake until the chicken is cooked through, about 20 minutes.
Meanwhile, in a saucepan, melt the butter over medium-low heat. Add the flour and stir to combine. Cook for 1 minute. Slowly whisk in the heavy cream. Sprinkle in the shredded Parmesan a little at a time (the more cheese you add the more parmesan flavor you will get) until melted and smooth. Season with garlic salt and pepper. Let simmer on very low heat until thickened. Do not let this boil or you will get a grainy sauce.
To serve, place a small amount of hot cooked pasta on a plate. Place the chicken braciole on the pasta and pour the Alfredo sauce over everything. Enjoy!!
Cook's Note: Most braciole recipes use beef and red tomato sauce, using chicken and Alfredo sauce in this one flips that idea upside down!