Preheat your oven to 180°C (350°F). Season the chicken breasts generously with salt, pepper, and a little paprika if desired. Use tongs to place each breast between two sheets of plastic wrap and pound gently to an even thickness—this helps them cook uniformly.
Heat a heavy skillet over medium-high heat until shimmering. Add olive oil and place the chicken breasts in the pan. Sear for about 3-4 minutes on each side until golden brown, then transfer to a baking dish and finish cooking in the oven for 10-15 minutes until the internal temperature reaches 75°C (165°F).
While the chicken cooks, add a tablespoon of butter to the same skillet and melt over medium heat. Toss in the sliced mushrooms and cook for about 5 minutes, stirring occasionally, until they release their moisture and turn deep brown.
Add the minced garlic to the mushrooms and cook for 30 seconds until fragrant, then pour in the white wine or chicken broth. Use a spoon to scrape up any browned bits from the bottom of the pan, intensifying the flavor.
Stir in the heavy cream, lemon zest, and thyme. Bring the mixture to a gentle simmer and cook for about 3 minutes until the sauce slightly thickens and coats the back of a spoon. Remove from heat and stir in the remaining butter for a shiny, silky finish.
Once the chicken is cooked through, remove from the oven and let rest for 5 minutes. Plate the chicken breasts and spoon the warm mushroom sauce generously over each piece. Garnish with additional chopped herbs if desired and serve immediately.
