Prep the chicken. Pat the chicken dry and season both sides with salt and pepper.
For even cooking, lightly pound breasts to an even thickness or use thighs as-is.
Crisp the bacon. Place chopped bacon in a large skillet over medium heat. Cook until crisp, 6–8 minutes. Transfer bacon to a plate and leave about 2 tablespoons of bacon fat in the skillet.
Sear the chicken. Increase heat to medium-high.
Add a little olive oil if the skillet looks dry. Sear chicken 4–5 minutes per side until golden. Remove to a plate; it will finish cooking in the sauce.
Sauté the mushrooms. Lower heat to medium.
Add mushrooms to the skillet with a small pinch of salt. Cook, stirring occasionally, until browned and their moisture evaporates, about 6–8 minutes.
Add garlic and herbs. Stir in minced garlic and thyme (or Italian seasoning). Cook 30–60 seconds until fragrant.
If the pan looks dry, add the butter now for a glossy finish.
Build the sauce. Pour in chicken broth, scraping up browned bits. Simmer 2 minutes to reduce slightly. Stir in heavy cream and bring to a gentle simmer.
Cheese and bacon. Stir in Parmesan until melted and smooth.
Add most of the bacon, reserving some for garnish. Taste and adjust salt and pepper. Add a pinch of red pepper flakes if you like heat.
Finish the chicken. Return chicken and any juices to the skillet.
Simmer on low 5–7 minutes, spooning sauce over the top, until chicken is cooked through (internal temp 165°F/74°C).
Brighten and serve. Squeeze a little lemon over the sauce to balance richness. Top with the remaining bacon and chopped parsley. Serve hot.