Cook the pasta: Bring a large pot of salted water to a boil. Add the penne pasta and cook according to the package instructions until al dente. Drain and set aside, reserving ½ cup of pasta water.
Cook the chicken: While the pasta cooks, season the chicken breasts with salt and pepper. Heat olive oil in a large skillet over medium heat. Cook the chicken for about 6-7 minutes per side, until golden brown and cooked through (165°F internal temperature). Remove from the skillet, let rest for a few minutes, then shred or slice.
Prepare the sauce: In the same skillet, add the minced garlic and sauté for 30 seconds until fragrant. Pour in the chicken stock and pesto, stirring to combine. Let simmer for 2 minutes.
Add the cream and cheese: Lower the heat and stir in the thickened cream and Parmesan cheese. Stir until melted and smooth.
Combine everything: Add the cooked pasta and shredded chicken back to the skillet. Toss to coat in the sauce. If needed, add a bit of reserved pasta water to loosen the sauce.
Add the spinach: Stir in the baby spinach and let it wilt from the heat of the pasta and sauce. Adjust seasoning with salt and pepper as needed.
Serve: Divide the pasta among plates and top with extra Parmesan cheese if desired. Enjoy!