Boil a large pot of well-salted water. Cook penne until al dente. Drain (don't rinse.) Toss drained penne with some olive oil to prevent sticking. Keep warm.
While pasta is preparing, make the chicken: Put cling wrap over each piece of chicken on a cutting board. Pound each piece evenly thin (about 1/4 inch thickness.) Sprinkle each chicken piece lightly and evenly with kosher salt and pepper, on both sides. Heat 2 TB of olive oil in a large skillet and brown two of the chicken breasts on both sides over medium high heat. Cook just until chicken is cooked through; about 2-3 minutes per side, depending on how cold and thick the chicken is. Repeat with remaining pieces. Slice chicken breasts into strips and set aside.
Put chopped onion and garlic into skillet with 2 TB oil. Saute 2-3 minutes until fragrant. Add the white wine and 1/2 tsp table salt. Boil vigorously until liquid is reduced by half, about 2 minutes.
Add fresh spinach and saute on medium-low, stirring often, just until spinach begins wilting. Turn heat to low. Add cooked chicken, cream, and pesto, stirring to combine and warm up, about 1 min. Remove from heat.
In a large serving bowl or dish, combine cooked penne with the chicken/spinach mixture. Season with more kosher salt and pepper to taste. Mix in fresh parmesan, reserving some for garnish. Serve immediately.
Notes
Wine Pairing Note: This pasta dish is perfect with a crisp, light Sauvignon BlancSource: Chew Out Loud, adapted from Simply Recipes