Slice the chicken breasts in half horizontally to create thin cutlets. Lightly season both sides with salt and pepper and set aside.
Prepare the garlic, shallot, and mushrooms so they’re ready to use.
Add the all-purpose flour, salt, pepper, garlic powder, onion powder, smoked paprika, and nutmeg to a large resealable bag. Seal and shake to combine.
Add the chicken, seal tightly, and shake until evenly coated. Set aside.
Heat 2 tablespoons of butter and the olive oil in a large, deep frying pan over medium-high heat. Shake any excess flour off the chicken, then sear for about 2 minutes per side, until golden. The chicken does not need to be fully cooked at this stage. Transfer to a plate.
Reduce the heat to medium-low. Add the remaining 2 tablespoons of butter, garlic, shallot, mushrooms, and fresh thyme. Sauté until the mushrooms have softened, stirring occasionally.
Stir in the balsamic glaze and white wine. Simmer for about 2 minutes, allowing the wine to reduce.
Add the chicken stock and heavy cream. Bring to a gentle simmer and cook for 2–3 minutes. Gradually whisk in the Parmesan cheese and simmer until the sauce thickens slightly. For a thicker sauce, add another 1–2 tablespoons of Parmesan. Taste and adjust the seasonings as needed.
Nestle the chicken back into the sauce, along with any juices from the plate. Simmer for 1–2 minutes, or longer as needed, until the chicken reaches an internal temperature of 165°F in the thickest part.
Garnish with fresh parsley, if desired, and serve with mashed potatoes, rice, or pasta.