Slice your chicken breasts lengthwise so you have two thin pieces for each breast. Place them between two pieces of parchment paper and pound them with a meat mallet so they are about ¼” thick. In a bowl, combine the flour, salt and pepper. Rub the flour mixture all over the sliced chicken.
Heat the 5 tablespoons (70g) of butter in a skillet over medium heat. Once the butter is melted and bubbling, add the sage leaves and garlic. Let the sage and garlic fry in the pan, gently moving it around the pan once or twice. Once the garlic begins to brown, remove it from the pan. Remove the sage from the pan when they begin to turn a little dark and crisp on the edges. By this point, you should have a nice garlic and sage infused brown butter. Swirl the bubbling browned butter around in the pan, then add the floured chicken breasts to the pan.
Let the chicken sear in the pan for 2-3 minutes. Flip the chicken over and sear for an additional 2-3 minutes. Add half of the chicken broth to the pan around the chicken and bring the broth to a simmer. Simmer for an additional 2 minutes, then add the lemon juice.
While the chicken is cooking, prepare the pasta according to the package instructions. Drain the pasta but don’t rinse it. Set it aside.
Add the capers to the pan with the chicken in it along with the remaining broth and browned garlic. Continue cooking the chicken until the internal temperature reaches 165 °F (74 °C) and the sauce has thickened. Remove the chicken and sauce from the pan and set aside.
Heat the remaining butter to the pan and let it melt and brown slightly. Add the pasta to the pan and toss it in the butter. Add the broth, capers, lemon juice and a few sliced lemon pieces. Season with salt and pepper to taste. Toss until the pasta is coated in the lemon butter sauce. The starch from the pasta will help to thicken any broth you add. If you find the pasta to be a bit dry, you can add a little more broth and toss until it’s well combined with the pasta.
Place the chicken back on top of the pasta in the pan and pour the sauce on top. Top with the sage, lemon slices and a sprinkle of salt and pepper