Season chicken breasts with salt, pepper, and paprika.
Heat olive oil in a large skillet over medium heat and sear chicken for 5 to 6 minutes per side until golden and cooked through. Remove and set aside.
Reduce heat and add 3 tablespoons of butter and 4 minced garlic cloves to the skillet. Sauté until fragrant, about 1 to 2 minutes.
Pour in ½ cup chicken broth and lemon juice, scraping the skillet bottom to deglaze. Add lemon zest and simmer the sauce for 3 to 4 minutes.
Return chicken to the skillet, spoon sauce over, and let simmer for 2 to 3 minutes.
In a medium saucepan, melt 1 tablespoon butter over medium heat. Add 2 minced garlic cloves and sauté briefly.
Stir in white rice and toast for 1 minute.
Add 2 cups chicken broth, bring to a boil, reduce heat, cover, and simmer for 15 minutes until rice is tender.
Remove rice from heat and stir in parmesan cheese and 1 tablespoon chopped parsley.
Serve chicken breasts over the garlic parmesan rice, spoon sauce on top, and garnish with extra parsley and red pepper flakes if desired.