Pound and season the chicken: If using breasts, lightly pound to an even thickness, about 1/2 inch.
Pat dry. Season both sides with salt, pepper, garlic powder, and paprika.
Dredge lightly: Sprinkle the flour on a plate. Lightly coat each piece, shaking off excess.
This helps with browning and gives the sauce a little body.
Sear the chicken: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high. Add chicken in a single layer. Cook 4–5 minutes per side until golden and just cooked through.
Transfer to a plate; tent with foil.
Sauté the garlic: Reduce heat to medium. Add the remaining 2 tablespoons butter. Stir in the garlic and cook 30 seconds until fragrant.
Avoid browning.
Build the sauce: Pour in the chicken broth, scraping up browned bits. Add lemon zest and lemon juice. Simmer 2–3 minutes to slightly reduce.
Make it silky: Stir in heavy cream if using, and add capers.
Simmer 1–2 minutes until the sauce lightly thickens. Taste and adjust seasoning.
Return the chicken: Nestle the chicken back into the pan and spoon sauce over the top. Simmer 1–2 minutes to warm through.
Finish and serve: Sprinkle with fresh parsley and garnish with lemon slices.
Serve with rice, mashed potatoes, pasta, or crusty bread.