Cook the spaghetti according to package instructions. Drizzle with olive oil, toss, and set aside.
Slice each chicken breast in half to form 4 thinner pieces of chicken. Coat each side generously with Italian seasonings and sprinkle with desired amounts of salt and pepper.
Combine the flour and Parmesan cheese together on a plate and coat both sides of the chicken, pressing down to ensure it sticks. This will ensure a crispy, golden coating.
Heat 2 Tablespoons of the olive oil in a large skillet (preferably cast iron) over medium-high heat.
Add 2 of the chicken pieces to the skillet to avoid overcrowding the pan. Sear the chicken on each side. Refrain from moving the chicken around as it sizzles, it will hinder the nice golden sear color. If the pan gets too hot, reduce the heat to medium. Each side will take 3-5 minutes. Once each side is a nice, golden brown and the middle is cooked, set the chicken aside. Add the remaining 2 Tablespoons of olive oil to the pan and cook the remaining 2 chicken pieces, then set aside.
Melt 2 Tablespoons of the butter in the pan. Add the garlic and cook for 60 seconds. Add the white wine and bring to a boil. Allow the white to reduce a bit, (about 5-6 minutes).
Add the remaining 2 Tablespoons of butter to the pan, along with the chicken broth, lemon juice, and capers. Scrape up any brown bits from the bottom of the pan to give the sauce plenty of flavor.
Whisk in the half and half and bring to a gentle bubble, then reduce the heat to low. Add the pasta to the pan and use tongs to toss it around in the sauce. Add the chicken back to the pan and use a spoon to drizzle extra sauce over the top of the chicken. Sprinkle with fresh parsley, and serve!