Heat the oil. Place a medium skillet over medium heat and add 2 Tbsp. extra-virgin olive oil.
Brown the chicken. Add the 2 (8-oz.) boneless, skinless chicken breasts cut into 1” pieces and season them with 3/4 tsp. salt. Cook for 4 to 5 minutes total, stirring occasionally, until the chicken is browned and an instant-read thermometer registers 160°. Transfer the chicken to a plate.
Cook the aromatics. Keep the same skillet over medium heat. Add the 4 finely chopped garlic cloves and 1/4 tsp. crushed red pepper flakes. Stir for about 30 seconds, until fragrant.
Create the pasta cooking liquid. Pour in 1 3/4 cups water and 3/4 cup heavy cream, then add 1/2 tsp. salt. Bring the mixture to a simmer.
Cook the penne in the skillet. Add 8 oz. penne to the simmering liquid. Cook for 8 to 10 minutes, stirring occasionally, until the pasta is al dente and the liquid has reduced into a sauce that coats the penne.
Return the chicken and add Parmesan. Stir in 1 oz. finely grated Parmesan, about 1/2 cup, along with the cooked chicken. Toss everything together for about 2 minutes, until the Parmesan has melted and the chicken is warmed through. Before serving, confirm that the chicken has reached a safe internal temperature of 165°F/74°C.
Fold in the pesto. Remove the skillet from the heat and fold in 2/3 cup store-bought or homemade pesto until evenly distributed throughout the creamy pasta.
Adjust the sauce. If the sauce feels dry, add water 1 Tbsp. at a time, tossing after each addition, until a creamy consistency forms. Taste and season with more salt if needed.
Finish with basil. Top the chicken pesto pasta with fresh basil if using, then serve.