Pat the chicken breasts dry with paper towels. Slice each breast horizontally into two thinner cutlets. Alternatively, place the chicken between sheets of plastic wrap and gently pound to an even thickness.
In a shallow bowl, combine the flour, salt, black pepper, and garlic powder.
Add 2 tablespoons butter and the olive oil to a large skillet. Heat over medium heat until the butter has melted.
Dredge the chicken cutlets in the seasoned flour, coating both sides and shaking off any excess.
Working in batches if necessary, arrange the chicken in the skillet without overcrowding. Cook for approximately 4–5 minutes on the first side until golden brown.
Flip and continue cooking for another 3–5 minutes, depending on thickness, until the chicken is cooked through. Transfer to a clean plate and loosely cover to keep warm.
Add the remaining 2 tablespoons butter to the skillet.
Add the sliced mushrooms in an even layer. Let them cook undisturbed until deeply browned on one side before stirring.
Continue cooking until the mushrooms release their moisture, the liquid evaporates, and the mushrooms develop a rich golden-brown color.
Add the sliced shallots and cook until softened and lightly caramelized.
Stir in the minced garlic and cook for approximately 30 seconds, just until fragrant.
Pour ½ cup chicken broth and the fresh lemon juice into the skillet. Scrape the bottom of the pan with a wooden spoon to release the flavorful browned bits.
Add the remaining 1½ cups chicken broth, fresh thyme, Dijon mustard, and heavy cream. Stir well and bring the sauce to a gentle boil.
Cook for approximately 5 minutes to allow the flavors to develop.
In a small bowl, whisk the cornstarch with 2 tablespoons cold water or broth until smooth. Gradually stir the slurry into the sauce.
Return the chicken and any accumulated juices to the skillet. Reduce to a gentle simmer and cook for approximately 5 minutes, or until the sauce thickens and the chicken reaches a safe internal temperature of 165°F (74°C).
Remove the thyme sprigs. Taste the Skillet Chicken and Mushroom Cream Sauce and adjust the salt and black pepper as needed.
Garnish with fresh parsley or additional thyme and serve warm.