Preheat the oven to 300°F (150°C).
In a pot of boiling salted water, cook the noodles according to package directions. While the pasta is cooking, warm the rolls and make the chicken.
Place the dinner rolls in the oven to warm.
Heat a non-stick pan over medium heat. While the pan is heating, prep the chicken.
Season both sides of the chicken well with salt and pepper. Sprinkle the flour onto a plate and place the chicken on top, turning to lightly coat completely, then shake off the excess.
Cook the chicken: Add the oil to the pan and sear the chicken on both sides to a deep golden brown. Remove the chicken and transfer to a plate.
In the same pan (see notes), add the broth, lemon juice, butter, and capers and bring to a simmer. Return the chicken to the pan and simmer for 5 minutes or until the chicken is cooked through. While the chicken finishes cooking, finish the buttered noodles.
Once the noodles are cooked, drain well and toss with butter in the pan. Season with salt and pepper to taste. Set pot over low heat to keep warm until you are ready to serve.
To serve: Spoon the buttered noodles onto a plate. Top with the chicken, pour the pan sauce over the top, and garnish with parsley and lemon. Enjoy with dinner rolls and milk.