Cook the pasta according to the package instructions, but pull it off the heat a few minutes early so it’s al dente. Drain it and set it aside.
While the pasta cooks, warm up a large Dutch oven or deep skillet over medium heat and add a swirl of oil to coat the bottom.
Sprinkle salt and pepper on the chicken breasts, then place them in the pan. Let them cook for about 4–5 minutes on each side until fully cooked.
Take the chicken out, let it rest on a cutting board for a few minutes, and then slice it thinly.
In a small bowl, mix the milk and flour together until smooth. Pour this into the pot and cook for about 2 minutes, stirring, until it starts to thicken.
Add the cream cheese and pesto, stirring constantly, until everything melts into a creamy sauce.
Toss the drained pasta, sliced chicken, and fresh spinach into the pot. Gently stir everything together until the spinach wilts.
Finish it off with a sprinkle of Parmesan cheese, a touch of parsley, and some freshly cracked black pepper.
Serve right away and enjoy!