01 - Generously season both sides of each chicken breast with 1 teaspoon salt, 1/2 teaspoon black pepper, and 1/2 teaspoon paprika, pressing the spices into the meat to adhere.
02 - Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add chicken breasts and sear for 3-4 minutes per side until golden brown. Transfer chicken to a plate and set aside.
03 - Reduce heat to medium. Add 2 tablespoons butter to the same skillet. Sauté chopped onion and sliced mushrooms for 3-4 minutes until softened and fragrant. Add minced garlic and cook for 30 seconds until aromatic.
04 - Sprinkle 2 tablespoons flour over the vegetables, stirring constantly for 1 minute to cook out the raw flour taste and form a roux base.
05 - Gradually whisk in 1 cup chicken broth, 1 cup whole milk, and 1/2 cup heavy cream, ensuring no lumps form. Add dried thyme, parsley, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Simmer for 2-3 minutes, stirring frequently, until slightly thickened. Stir in Parmesan until melted and smooth.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Cover and reduce heat to low. Cook for 15-20 minutes until chicken reaches an internal temperature of 165°F and is cooked through.
07 - Rinse rice under cold water until water runs clear. In a medium saucepan, bring 3 cups water or broth and 1/2 teaspoon salt to a boil. Add rice, cover, reduce heat to low, and simmer for 15-18 minutes until tender. Remove from heat and let stand, covered, for 5 minutes. Fluff with a fork before serving.
08 - Spoon fluffy rice onto each serving plate. Top with a chicken breast and generously spoon the creamy sauce over both the chicken and rice. Garnish with additional parsley if desired.