Pound the chicken breasts to an even thickness, about ⅓" thick. Season the chicken medallions with salt and pepper. Dust them with the flour and shake off excess. Heat the oil in a large saucepan or skillet to a shimmer on medium heat. Add the chicken and cook until golden on each side - this will take about 3-4 minutes each side. Set them aside wrapped in foil, or on a plate in a toaster oven set to warm (again, covered with foil). Remove excess oil from the skillet, but leave a little for the garlic. Add the garlic, and cook until fragrant - no more than 30 seconds.
Add the broth or stock and scrape the pan to loosen any fond (brown bits) from the bottom. This is flavor!
Add the lemon slices and bring the mixture to a boil. Continue to cook, stirring occasionally, until the broth is reduced to about 1½ cups.
Add the lemon juice, wine, and capers. Once it begins simmering, continue cooking until it has reduced just a bit, stirring frequently to speed the reduction process. Don't over-reduce to the point that you don't have enough sauce to spoon over the chicken and pasta.
Now add the butter and parsley. Stir gently to incorporate it into the sauce.
Serve over pasta (my personal choice), rice, or with a side of garlic roasted potatoes, with the sauce spooned over each portion and garnished with the remaining parsley.