Preheat and prep: Heat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Sauté the mushrooms: Heat butter and olive oil in a large skillet over medium-high.
Add sliced mushrooms and a pinch of salt. Cook 6–8 minutes, stirring occasionally, until golden and most liquid has evaporated.
Add aromatics: Reduce heat to medium. Stir in the onion and cook 3–4 minutes until softened.
Add the garlic and cook 30 seconds, just until fragrant.
Build the sauce: Pour in the chicken broth and scrape up any browned bits from the pan. Stir in the heavy cream and bring to a gentle simmer.
Melt in the cheeses: Add cream cheese in small chunks, stirring until smooth. Mix in the Parmesan, thyme, smoked paprika, and a few grinds of black pepper.
Simmer 2–3 minutes to slightly thicken. Taste and adjust salt.
Add greens (optional): Stir in the chopped spinach and cook 1–2 minutes until wilted.
Combine with chicken: Fold the cooked chicken into the sauce until evenly coated.
Assemble: Transfer the mixture to the prepared baking dish. Spread evenly and top with shredded mozzarella.
Bake: Bake 18–22 minutes, until the casserole is bubbling and the cheese is melted and lightly golden.
Rest and serve: Let it rest 5–10 minutes before serving so the sauce sets slightly.
Sprinkle with extra thyme or chopped parsley if you like.