Pat the chicken breasts dry with paper towels. Slice each breast horizontally to create two thinner chicken cutlets. Alternatively, place the chicken between sheets of plastic wrap and gently pound to an even thickness.

Combine the flour, salt, black pepper, and garlic powder in a shallow bowl.

Heat 2 tablespoons butter and the olive oil in a large skillet over medium heat.

Dredge the chicken cutlets in the seasoned flour, coating both sides and shaking off any excess.

Working in batches if necessary, place the chicken in the hot skillet. Cook for about 5 minutes on the first side, then turn and cook for another 3–5 minutes, or until golden and cooked through. Transfer to a plate and keep warm.

Melt the remaining 2 tablespoons butter in the same skillet. Add the sliced mushrooms and let them cook undisturbed until deeply browned on one side.

Stir the mushrooms and continue cooking until they release their moisture, the liquid evaporates, and the mushrooms become nicely browned.

Add the shallots and cook until softened and beginning to caramelize. Stir in the garlic and cook for about 30 seconds, just until fragrant.

Pour 1/2 cup chicken broth and the lemon juice into the skillet. Scrape the browned bits from the bottom of the pan with a wooden spoon.

Add the remaining 1 1/2 cups chicken broth, thyme, Dijon mustard, and heavy cream. Bring the mixture to a gentle boil and cook for about 5 minutes.

Combine the cornstarch with 2 tablespoons water or broth until smooth. Stir the slurry into the sauce.

Return the chicken to the pan and gently simmer for about 5 minutes, until the sauce has thickened and the chicken reaches an internal temperature of 165°F (74°C).

Remove the thyme sprigs. Taste and adjust the salt and black pepper as needed.

Garnish the Skillet Chicken and Mushroom with fresh parsley or thyme and serve warm.