Preheat oven to 375°F.
Season the chicken breasts with garlic powder, paprika, salt, and pepper on both sides.
In a large ovenproof skillet, heat the olive oil over medium-high heat. Add the chicken breasts and sear on both sides until golden brown, about 2-3 minutes per side. You may need to cook in batches. Place the chicken on a plate and set aside.
In the same skillet, add the butter and melt over medium heat. Add the chopped onion and sauté until translucent, about 3 minutes. If you have a lot of browned bits on the bottom of the pan from the chicken, deglaze with a splash of the chicken broth.
Add the minced garlic and sliced mushrooms, cooking until the mushrooms are browned and any liquid has evaporated.
Stir in the thyme and rosemary, cooking for another minute.
Pour in the white wine and cook until the liquid has reduced by half.
Sprinkle the flour over the mushroom mixture, stirring constantly to combine and cook out the raw flour, about 2 minutes.
Gradually whisk in the chicken broth and heavy cream, bringing the mixture to a simmer until thickened.
Stir in the grated Parmesan cheese until melted and smooth. Season with aditional salt and pepper, to taste.
Return the seared chicken breasts to the skillet, nestling them into the mushroom sauce. Transfer the skillet to the preheated oven and bake for 20 minutes, or until the chicken is cooked through. Timing will depend on the thickness of the chicken breasts and how long you seared them. We always recommend checking with a meat thermometer and cooking until the temperature reaches 165°F.
Allow the dish to rest for a few minutes before serving.