Slice chicken breasts in half lengthwise to create thinner cutlets. Pat completely dry with paper towels and season both sides generously with salt and pepper.

Heat a 12-inch skillet over medium-high heat. Add butter and olive oil. Once butter melts and foams, add sliced mushrooms in a single layer. Let cook undisturbed for 2-3 minutes to develop golden color. Stir once, then cook another 2 minutes until nicely browned. Remove to a plate.

In the same skillet, add chicken cutlets. Sear for 3-4 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to plate with mushrooms and let rest 2-3 minutes.

Add more butter to skillet if needed. Add minced garlic and sauté for 30 seconds until fragrant. Pour in lemon juice and scrape up browned bits from bottom of pan.

Add chicken broth, Dijon mustard, and return mushrooms to skillet. Simmer for 2-3 minutes. Stir in heavy cream, then slowly add cornstarch slurry while stirring. Let sauce bubble and thicken for 1-2 minutes until it coats the back of a spoon.

Return chicken to skillet and spoon sauce over top. Simmer gently for 2-3 minutes to heat through. Taste and adjust seasoning. Garnish with fresh herbs and serve immediately.