Step 1

Coat the chicken with flour. Place the flour, salt, and pepper in a wide, shallow bowl and whisk to combine. Dredge the chicken in the flour and shake off any excess.

Step 2

Cook the chicken. Heat 2 tablespoons of the butter and the oil in a 10-inch or larger skillet over medium-high heat until shimmering. Add the chicken in batches if needed and cook until lightly browned, about 3 minutes per side. Transfer the chicken to a paper towel-lined plate. Repeat with any remaining cutlets if needed.

Step 3

Add the lemon slices. Slice half the lemon into thin slices and remove the seeds. Add the lemon slices to the skillet and cook until fragrant, about 30 seconds.

Step 4

Simmer the broth. Add the broth and simmer until slightly reduced, about 3 minutes.

Step 5

Finish the sauce and chicken. Reduce the heat to low and stir in the remaining 2 tablespoons butter, capers, and lemon juice from the remaining lemon half. Return the chicken to the skillet and cook until the sauce is thickened and the chicken is heated through, 3 to 4 minutes. Garnish with parsley before serving.