In a large pot of salted boiling water, cook the penne pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta cooking water.
In a large skillet, heat olive oil over medium-high heat. Add the diced chicken breasts, season with salt and pepper, and sauté until cooked through and golden brown, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the baby spinach and sauté for 2-3 minutes until wilted. Reduce the heat to medium-low and add the heavy cream, stirring to combine.
Stir in the basil pesto and grated Parmesan cheese until smooth and combined. If the sauce is too thick, add a splash of the reserved pasta cooking water until you reach your desired consistency.
Add the cooked penne pasta and sautéed chicken to the skillet, along with the chopped sun-dried tomatoes. Toss everything together and cook for an additional 2-3 minutes to heat through and meld the flavors.
Plate the creamy pesto chicken pasta and garnish with fresh basil leaves and extra Parmesan cheese if desired.