Pound chicken breasts to 1/2-inch thick.

Mix 1/2 cup flour, lemon zest, salt, and pepper in a shallow bowl. Dredge chicken in flour mixture.

Heat olive oil in a skillet over medium-high. Cook chicken 4–5 min per side until browned and cooked through. Set aside.

Lower heat to medium. Melt butter in the same skillet. Add garlic and cook 30 seconds.

Whisk in 1 1/2 tablespoons flour, cook 2 min, scraping up brown bits.

Gradually add chicken broth, whisking until smooth.

Add lemon juice, extra zest, white wine, and capers. Simmer 3 min.

Return chicken to skillet. Simmer in sauce 2–3 min until heated through. Season with salt and pepper.

Stir in parsley.

Serve chicken and sauce over cooked angel hair pasta. Garnish with lemon slices and Parmesan if desired.