Pat the chicken breasts dry with paper towels. Cut each breast in half diagonally into 2 thinner cutlets. Alternately, place the chicken breasts between two sheets of plastic wrap and pound to an even thickeness.
In a shallow bowl combine the flour, salt, pepper and garlic powder. Set aside.
Add 2 tablespoons butter and 1 tablespoon olive oil to a large skillet. Heat over medium until the butter is melted. Dredge 3 chicken cutlets in the flour mixture, coating both sides, shaking off the excess flour. Add the coated chicken to the skillet and cook until lightly browned, about 5 minutes. Turn and cook another 3-5 minutes. Remove the cooked chicken to a plate and cover to keep warm. Repeat until all chicken is browned.
Add remaining 2 tablespoons butter to the pan and heat until melted. Add the sliced mushrooms and cook, undistrubed, until the mushrooms are well browned on one side. Stir and turn the mushrooms and continue cooking until the moisture is released and evaporated, and the mushrooms are all well browned.
Add the sliced shallots to the pan and cook until softened. Add the minced garlic and sauté for 30 seconds or until fragrant. Pour the wine into the pan and scrape the bottom to deglaze. Add the thyme sprigs, chicken broth, mustard and cream. Bring to a boil and cook for 5 minutes. Stir in the dissolved cornstarch. Bring the sauce back to a light simmer and add the chicken. Heat and simmer for 5 minutes or until the sauce is thickened and the chicken warmed through. Remove the thyme sprigs, and season the dish with salt and pepper to taste.
Garnish with parsley or additional thyme and serve with rice, potatoes or noodles.