1: Slice the lemon in half, juice one half, then cut the other half into 1/8" slices and set aside.
2: Trim any excess fat from the chicken breasts and slice in half lengthwise.
3: Season both sides of the chicken breasts evenly with kosher salt and freshly ground black pepper, then dredge each breast in the flour, shaking off any excess.
4: Heat 2 tablespoons of butter with canola oil in a large skillet over medium-high heat.
5: Add 4 pieces of the chicken and cook for 2-3 minutes per side. Transfer to a platter or sheet pan and cover with foil. Continue with the remaining chicken.
6: Reduce the heat to medium and add chicken broth or wine, the lemon juice, sliced lemons, and capers, scraping up the browned bits on the pan and cook for 2-3 minutes.
7: Stir in the remaining 1 tablespoon of butter until melted. Taste for seasoning and spoon the sauce over the chicken breasts.
8: Serve with mashed potatoes or cauliflower, polenta, or noodles.
