Pound chicken breasts until very thin, then season both sides liberally with kosher salt and black pepper. Add flour to a shallow plate, whisk eggs with milk in a large shallow dish, and add breadcrumbs to a separate large shallow plate. Dredge both sides of each chicken breast first in the flour, then dip in the egg mixture, then press both sides into the breadcrumbs until evenly coated. Set coated chicken breasts on a plate.
4 chicken breasts, kosher salt, black pepper, ½ cup flour, 4 eggs, ¼ cup milk, 2 cups breadcrumbs
Heat ⅛ cup olive oil in a large skillet over medium high heat. Once a speck of flour sprinkled into the oil sizzles, add 2 chicken breasts, cooking until breadcrumbs are golden, 3-4 minutes. Flip and continue cooking until chicken is cooked through, an additional 3-4 minutes or more depending on thickness. Repeat with remaining olive oil and chicken. Set cooked chicken aside and keep warm.
¼ cup olive oil
Bring a large pot of salted water to a boil. Cook linguine (or other long pasta) according to package directions until just al dente.
10 ounces linguine
Meanwhile, in a new large skillet, melt butter over medium heat. Season with black pepper and add zest of the lemon, sautéing for 1-2 minutes. Add chicken broth, lemon juice, and capers, simmering for 3-4 minutes.
black pepper, 4 tablespoons butter, 1 lemon, 1½ cups chicken broth, ½ cup capers
Drain pasta and add directly to skillet with sauce. Toss until coated, then divide between plates.
Top each plate with a breaded chicken breast, then top with remaining sauce and additional lemon zest.