Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat. Season the chicken with kosher salt and freshly ground black pepper, then cook for 3–4 minutes until lightly browned; transfer it to a plate if the pan is crowded.

Add the minced garlic to the same pan and cook for 30–60 seconds, stirring constantly, just until fragrant. Do not let the garlic become deeply brown, since it can turn bitter.

Pour in the chicken stock and milk, then stir in the uncooked penne. Return the browned chicken and any juices from the plate to the pan.

Bring the mixture to a boil, reduce the heat, cover, and simmer for approximately 15 minutes. Stir every few minutes so the pasta cooks evenly and does not stick, continuing until the pasta is tender and the chicken reaches 165°F internally.

Remove the pan from the heat and stir in the basil pesto and freshly grated Parmesan. If the sauce is too thick, loosen it with a small amount of milk or broth.

Serve the pasta immediately with chopped fresh basil and additional Parmesan if desired. Spoon plenty of sauce over each portion so every bite includes chicken, pasta, and pesto.