Prep the chicken: Pat chicken dry and cut into large bite-size pieces. Season with 1 teaspoon salt, 1/2 teaspoon pepper, and Italian seasoning if using.
Heat the pan: Set a large skillet over medium-high heat.
Add 1 tablespoon olive oil and 1 tablespoon butter.
Sear the chicken: Add chicken in a single layer. Don’t crowd. Cook 4–5 minutes per side until browned and just cooked through.
Transfer to a plate and tent loosely.
Sauté the mushrooms: Add remaining olive oil and 1 tablespoon butter. Toss in mushrooms and a pinch of salt. Cook, undisturbed, 2 minutes to get color, then stir and cook 4–6 minutes until golden and their moisture evaporates.
Aromatics in: Lower heat to medium.
Add shallot and cook 1–2 minutes until soft. Stir in garlic for 30 seconds until fragrant.
Build the sauce: Add heavy cream and Dijon. Stir in thyme and red pepper flakes if using.
Simmer gently 2–3 minutes to thicken slightly.
Add cheese: Sprinkle in Parmesan and stir until melted and smooth. Taste and adjust salt and pepper. If too thick, splash in a little chicken broth or water.
Finish with chicken: Return chicken and any juices to the skillet.
Simmer 2 minutes to warm through and marry flavors.
Brighten and serve: Squeeze a little lemon over the top (optional). Garnish with parsley. Serve over cauliflower rice or with sautéed greens.