Season chicken with salt and pepper and dredge lightly in flour, shaking off excess. Bring a large pot of salted water to a boil for the spaghetti and cook according to package directions until al dente. Reserve 1 cup pasta water and drain.

Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook chicken in batches 2–3 minutes per side until golden and cooked through. Transfer to a plate and tent with foil.

Reduce heat to medium and add garlic to the skillet, cooking 30 seconds. Add chicken broth (or wine), scraping up browned bits. Stir in lemon juice and capers and simmer 3–4 minutes to reduce slightly.

Whisk in remaining butter to create a silky sauce. Add reserved pasta water if needed to achieve desired consistency. Taste and adjust seasoning.

Toss spaghetti with the sauce, add chopped parsley and lemon zest if using. Nestle chicken on top or slice and toss through the pasta. Serve immediately.