In a bowl combine the lemon slices, garlic halves, and sugar and set aside.
Place a chicken breast between two pieces of plastic wrap and pound with a heavy skillet or rolling pin until about ¾-inch thick. Repeat with remaining chicken breasts.
Sprinkle ½ teaspoon kosher salt and pepper on both sides of all of the breasts. Heat the olive oil over medium high heat in a large skillet and cook the chicken for 5 minutes on each side until done all the way through. Remove the chicken from the skillet and keep warm.
Add the sliced lemon mixture to the pan and cook until for one minute or until the lemons begin to brown. Return them back to the bowl.
Wipe out the skillet with paper towels and return to medium heat. Add 1 tablespoon of butter to the pan along with the shallot, minced garlic, oregano and thyme. Cook for 1 minute. Add the wine to the pan and scrape up any browned bits on the bottom. Reduce the wine until nearly evaporated. Add in ½ teaspoon kosher salt, chicken stock, and flour and whisk together. Bring to a simmer and cook until sauce has reduced and is slightly thick. Remove from the heat. Whisk in remaining butter and capers. Return the chicken and any juices to the pan and turn to coat in the sauce. Top the chicken with the lemon slices and parsley. Serve with noodles and fresh asparagus.