Fill your large cooking pot with plenty of water. Toss in a generous pinch of salt for flavor. Bring the water to a rolling boil over high heat.
Drop your penne pasta into the boiling water carefully. Stir the noodles occasionally so they do not stick. Cook them until they are slightly firm. Drain the water using your colander.
Cut your chicken breasts into small, bite-sized cubes. Melt your butter in the large skillet over medium heat. Add the chicken pieces to the hot skillet safely.
Cook the chicken cubes for about seven minutes. The meat should turn white and have no pink spots. Remove the chicken from the skillet and set aside.
Mince your garlic cloves into the same warm skillet. Cook the garlic for one minute until it smells great. Pour the heavy cream into the skillet slowly.
Bring the heavy cream to a very gentle simmer. Stir in the grated parmesan cheese until it dissolves completely. The sauce will begin to thicken up nicely.
Dump the cooked pasta back into the skillet. Add the cooked chicken pieces to the sauce too. Toss everything together so the noodles are fully covered.
Pour the creamy pasta mixture into your baking dish. Arrange slices of provolone cheese across the top surface. Turn your oven broiler to high heat mode now.
Place the baking dish under the hot broiler carefully. Cook for three to five minutes until cheese bubbles. Watch it closely so the top does not burn.
Remove the hot dish from the oven using mitts. Sprinkle chopped fresh parsley over the melted cheese layer. Let it cool for five minutes before serving.