Bring a large pot of heavily salted water to a boil.
While the water heats, mince the garlic and grate the Parmesan cheese. Pat the chicken breasts dry and cut them into 1-inch cubes. Season with 1/2 teaspoon kosher salt and black pepper.
Once boiling, add the penne pasta and cook until al dente, about 10-12 minutes.
In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Add the seasoned chicken cubes and cook until browned on all sides, about 5-8 minutes.
Add the minced garlic to the skillet and cook for about 30 seconds until fragrant.
Reserve about 1/2 cup of pasta water before draining the pasta. Add the heavy cream and basil pesto to the skillet and bring to a gentle simmer. Let it simmer for 6-8 minutes to thicken the sauce.
Toss the drained pasta and baby spinach into the sauce, stirring until the spinach wilts, about 1-2 minutes. Adjust seasoning with more salt if needed.
Serve your chicken pesto pasta garnished with additional grated Parmesan and fresh basil leaves if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3-4 days. Reheat gently on the stovetop.