Gather all ingredients.
Place each chicken breast between 2 sheets of parchment paper or plastic wrap; pound with a meat mallet or heavy skillet to a ¼-inch thickness.
Sprinkle chicken evenly with garlic powder and ½ teaspoon each salt and pepper. Pour flour into a shallow dish; dredge chicken in flour, shaking off excess.
Heat oil and 1 tablespoon butter in a large cast-iron or stainless steel skillet over medium-high. Add 2 chicken breasts to pan. Cook until browned and just cooked through, about 3 minutes per side. Remove cooked chicken to a plate and repeat process with remaining 2 chicken breasts; remove cooked chicken to the plate.
Melt remaining 1 tablespoon butter in pan over medium-high heat. Add mushrooms to pan; sauté until mushrooms release liquid and begin to brown, about 3 minutes. Stir in garlic and shallots; cook until shallots soften, stirring frequently, 1 to 2 minutes.
Stir in chicken stock and wine, scraping bottom of pan to loosen any browned bits. Add thyme and remaining ½ teaspoon salt and ¼ teaspoon pepper. Cook until liquid reduces by about half, 5 to 6 minutes.
Stir in cream; cook until slightly thickened, 3 to 4 minutes. Discard thyme sprigs.
Return chicken to pan; cook until thoroughly heated, about 2 minutes. Serve chicken with sauce. Garnish with thyme leaves, if desired.
