Bring a large pot of salted water to a rolling boil. Add the penne pasta and cook according to package instructions until al dente, about 10-12 minutes. Reserve 1 cup of pasta water, drain remaining, and set aside.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add bite-sized pieces of chicken and sauté for 5-7 minutes until golden brown. Remove chicken and set aside.

In the same skillet, add another tablespoon of olive oil if needed, and toss in the chopped onion. Sauté for 5 minutes until it becomes translucent.

Add minced garlic and cook for 1 minute, stirring constantly until aromatic.

Pour in crushed tomatoes, heavy cream, and vodka. Mix well and simmer for 5-6 minutes until sauce thickens.

Return chicken to skillet, season with salt and pepper, and let simmer for 5-10 minutes.

Add cooked penne pasta to the skillet and toss to coat. Stir in reserved pasta water as needed to adjust consistency.

Stir in grated Parmesan cheese until melted and creamy. Serve hot, garnished with fresh basil.