Pat the chicken breasts dry using paper towels. Each breast should be cut horizontally in two equal pieces. Alternately, place each breast between 2 sheets of plastic wrap. Pound the chicken breasts until they are uniformly thick.

Combine the flour, salt and pepper in a small bowl. Set aside.

In a large skillet, add 2 tablespoons butter and 1 teaspoon olive oil. Heat on medium heat until butter melts. Dip 3 chicken cutlets into the flour mixture. Cover both sides with the mixture and shake off any excess flour. Cook the chicken in the flour mixture until it is well browned. Cook for another 3 to 5 minutes. Transfer the chicken to a plate. Cover with a towel to keep warm. Continue until all the chicken is brown.

Heat the remaining butter in a saucepan until it melts. Cook the sliced mushrooms until they are very dark one side. Continue to stir the mushrooms, then turn them over and cook until all the moisture has evaporated.

Place the shallots in a pan. Cook until they are softened and begin to brown. Sauté the minced garlic for about 30 seconds, or until fragrant. Pour the wine in the pan. Scrape the bottom to remove any stray bits. Add the cream, chicken broth, mustard, and thyme sprigs. Bring to boil. Cook for 5 minutes. Mix in the dissolved cornstarch. The chicken should be added to the sauce. Let the sauce thicken and the chicken warm through for five minutes. Season the dish with salt to taste by removing the thyme sprigs.

Serve with potatoes, rice or noodles garnished with parsley or additional Thyme.