Season the chicken breasts with salt, pepper, paprika, and thyme on both sides.
In a large skillet, heat olive oil over medium-high heat. Add the chicken breasts and sear for about 6-7 minutes on each side, until golden brown and cooked through. Remove from the skillet and set aside.
In the same skillet, add the chopped onion and cook for about 3-4 minutes until translucent. Then, add the minced garlic and sliced mushrooms, cooking for an additional 5-6 minutes until the mushrooms are soft and browned.
Pour in the chicken broth, stirring to scrape up any brown bits from the bottom of the skillet. Bring to a simmer, then reduce the heat. Add the heavy cream and stir until well combined. Allow to simmer for about 3-4 minutes until the sauce thickens slightly.
Return the cooked chicken breasts to the skillet, spooning the creamy mushroom sauce over them. Cook for another 2-3 minutes to heat through, then adjust seasoning with salt and pepper if needed.
Remove from heat, and sprinkle with fresh chopped parsley before serving.