In a medium saucepan, melt 1 tablespoon butter over medium heat. Add minced garlic and cook 30–45 seconds. Add rinsed rice and stir 1 minute. Add 2 cups chicken broth, bring to a boil, then reduce to low, cover, and simmer 15–18 minutes until tender. Remove from heat, fluff, stir in Parmesan, and season.
Season chicken with salt and pepper. Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook chicken 4–5 minutes per side until golden and cooked through. Remove and tent with foil to rest.
Reduce heat to medium. Add 4 tablespoons butter to the skillet, then add minced garlic and cook 30–45 seconds. Deglaze with 1/3 cup broth, scraping up browned bits. Simmer 2–3 minutes. Stir in lemon juice, lemon zest, red pepper flakes, and parsley.
Slice the rested chicken and return to the skillet for 1 minute to coat in sauce. Serve chicken over garlic Parmesan rice and spoon extra sauce over the top. Garnish with parsley and lemon wedges.
Notes
Make-ahead: Cook rice in advance and reheat before serving; add Parmesan fresh when reheating.
For richer sauce: Stir in 1–2 tablespoons of heavy cream at the end.
To keep chicken juicy: Pound breasts to even thickness and avoid overcooking.