Preheat your oven to 200 F and place baking sheet on middle rack.
Put flour in shallow bowl. Pat the chicken down with paper towels and season with salt and pepper. Coat each piece lightly in the flour and shake off any excess.
Heat the oil in a large skillet over medium high heat. Working in batches (I did 2 batches of 4 pieces), add chicken to skillet and brown on both sides, about 2 minutes per side. They'll cook pretty quick because they're somewhat thin. After each piece is done, place on baking sheet in the oven to keep warm. Repeat until all chicken is complete.
Add the shallot and garlic to the skillet and cook until soft, about 2 minutes. Thinly slice one half of the lemon and cut into half moons. Add the lemon slices, along with the chicken broth to the pan and scrape up any sucs (brown bits). Simmer this mixture until slightly thickened, about 8 minutes.
Stir in the white wine and squeeze juice from leftover lemon half into the skillet. Turn the heat down to low and stir in butter pats, one at a time. Turn off the heat and stir in the parsley. Season with salt and pepper to taste.
Serve with sauce on top of chicken. I also braised some spinach really quick in some chicken stock. Andy kept raving how it went exceptionally well with the chicken piccata itself.