Bring a large pot of salted water to a boil.
Cook the penne pasta according to the package directions until al dente. Drain and set aside.
For an even creamier sauce, reserve about 1/2 cup of pasta water before draining. You can use a splash later if you need to loosen the sauce.
Dice the chicken into bite-sized pieces and add it to a mixing bowl.
Season with salt, black pepper, and Italian seasoning. Toss until the chicken is evenly coated.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the seasoned chicken and cook for approximately 8–10 minutes, stirring occasionally, until the chicken is golden brown and cooked through to an internal temperature of 165°F.
Transfer the cooked chicken to a clean bowl and set aside.
Reduce the skillet to medium heat.
Using the same skillet, melt 2 tablespoons butter. Add the minced garlic and cook for 1–2 minutes, stirring frequently, until fragrant.
Pour in the heavy cream and stir to combine.
Bring the cream to a gentle simmer and cook for approximately 5 minutes, whisking frequently. The sauce should begin to thicken slightly.
Stir in the basil pesto until completely incorporated.
Gradually add the Parmesan cheese, stirring until the cheese has melted and the sauce is smooth and creamy.
Taste the sauce and add up to 1/2 teaspoon salt, if needed.
Return the cooked chicken to the skillet and stir to coat it in the creamy pesto sauce.
Add the cooked penne pasta and gently toss everything together until the pasta and chicken are evenly coated.
If the sauce becomes thicker than you'd like, add a small splash of reserved pasta water until it reaches your desired consistency.
Serve immediately with additional Parmesan cheese and basil pesto, if desired.