Preheat the oven. Set to 375°F (190°C). Grease a 9x13-inch baking dish or similar.
Season the chicken. Pat the pieces dry.
Season with salt, pepper, and paprika. This step builds flavor and helps browning.
Brown the chicken. Heat a large skillet over medium-high. Add a swirl of olive oil.
Sear the chicken in batches, 2–3 minutes per side, until lightly golden. It doesn’t need to be cooked through. Transfer to a plate.
Sauté the mushrooms. Add 1 tablespoon butter to the skillet.
Drop in the mushrooms with a pinch of salt. Cook undisturbed for 2–3 minutes, then stir. Continue until they release liquid and turn deep golden, about 7–8 minutes.
Remove to the plate with the chicken.
Cook the aromatics. Add remaining butter to the skillet. Sauté onion until soft and translucent, 3–4 minutes. Stir in garlic for 30 seconds, just until fragrant.
Make the roux. Sprinkle in the flour.
Stir for 1 minute to cook off the raw taste. Gradually whisk in the chicken broth to avoid lumps, scraping up browned bits from the pan.
Finish the sauce. Lower the heat. Stir in heavy cream, thyme, Dijon, and lemon juice.
Simmer 2–3 minutes until slightly thickened. Taste and season with salt and pepper. Stir in half of the parmesan.
Combine in the dish. Add the browned chicken and mushrooms to the sauce and fold gently.
If using cooked rice or pasta, stir it in now. Transfer everything to the prepared baking dish.
Top and bake. Mix remaining parmesan with bread crumbs, a drizzle of olive oil, and a pinch of salt. Sprinkle over the casserole.
Bake 18–22 minutes, until bubbling at the edges and the top is lightly crisp.
Rest and serve. Let stand 5–10 minutes so the sauce sets slightly. Sprinkle with parsley and serve warm.