PREP CHICKEN: Cut chicken breasts in half widthwise to get 4 pieces. Use a meat mallet/frying pan/your fist to give each piece a quick pound (don't flatten chicken, we just want all the pieces fairly even in width). Season both sides with salt, pepper, and Italian seasoning. I add about 1/4 teaspoon of each seasoning to one side, flip and add another 1/4 teaspoon of each seasoning to the other side.
PASTA: Set a large colander in the sink with a glass mug or liquid measuring cup in the center of the colander (this is so you don't forget to grab some pasta water before draining the pasta!). Bring a large pot of water to a boil. Generously salt the water and then cook the pasta according to package instructions subtracting 1 minute from what the package indicates. Use the glass mug to remove a big scoop of pasta water (set aside for now) and then drain the pasta and set aside. Don't rinse under cool water.
COOK CHICKEN: Meanwhile, add 2 tablespoons butter to a large heavy bottom skillet. Heat to high heat and once melted, add in the chicken in one layer. Cook for about 2-3 minutes per side or until cooked through (registers 160 degrees/juices run clear) and remove to a plate. Tent with foil and set aside for now.
GARLIC: Reduce heat to medium. Add the remaining 1 tablespoon butter to the skillet. Once melted, add garlic. Cook, until golden, stirring constantly, about 30 seconds. Pour in 1/2 cup of chicken broth. It should sizzle and boil, scrape up any browned bits off the bottom of the pan. Once this 1/2 cup is mostly evaporated, add in the other 1/2 cup. Stir.
CREAM SAUCE: Add in the heavy cream, Parmesan cheese, sun-dried tomatoes, and remaining 1 teaspoon Italian seasoning. Simmer, over medium-heat, stirring occasionally for 3-5 minutes or until it thickens up and slightly reduces. Sauce shouldn't boil, reduce heat/stir more frequently it needed. While it is thickening, dice the chicken into small pieces or shred with 2 forks on the plate.
TOSS: Add the spinach, chicken (and any juices left behind on the plate!) and pasta. Use tongs to toss ingredients into the cream sauce until the sauce thickens, nicely coats the pasta, and the spinach cooks down (1-2 mins). IF needed (sauce is too thick), slowly add in that set aside pasta water. After tossing for about a minute, add in the pesto and continue to toss. Taste and adjust adding more salt/pepper to taste.
SERVE: Serve immediately. Top individual plates with a touch more Parmesan if desired, and fresh herbs if using. Enjoy immediately! Pasta is best enjoyed right after being tossed!