Heat grill or grill pan to medium-high heat. Rub chicken breasts on all sides using 2 tablespoons olive oil. Sprinkle with half of the salt and black pepper.
Grill chicken and cook without moving for 3 minutes. Turn chicken one-quarter turn and continue to cook 2 to 3 minutes. Flip the chicken. Allow chicken to rest for at least 5 minutes. Slice before serving.
In a large (12-inch) skillet over medium heat, add the remaining olive oil and butter. Allow the butter to melt and then add the garlic and onion and cook until the onion is softened.
Carefully add the vodka to the skillet and bring to a boil. Cook for 2 minutes. Stir in the crushed tomatoes and remaining seasonings. Reduce heat to the lowest setting and stir in the heavy cream..
Add the cooked penne to the skillet and carefully toss in the sauce. Serve topped with grilled chicken and grated parmesan cheese.