Heat a tablespoon of oil or butter in a large heavy-bottomed pot over medium heat until shimmering. Add the chopped onion and cook, stirring occasionally, until translucent and fragrant, about 5 minutes.
Add the sliced mushrooms to the pot and cook, stirring frequently, until they release their juices and turn a deep brown, about 8 minutes. The mushrooms should smell earthy and look richly browned.
Push the mushroom mixture to one side of the pot. Add the diced chicken breasts to the empty side and cook, stirring occasionally, until they are browned and cooked through, about 4-5 minutes. The chicken should reach an internal temperature of 75°C (165°F).
Pour in the chicken broth, scraping the bottom of the pot to loosen any browned bits. Bring the mixture to a gentle simmer, then reduce the heat to low and let it simmer uncovered for about 15 minutes to meld the flavors and slightly reduce.
Stir in the heavy cream and thyme, then season with salt and pepper to taste. Continue cooking on low for another 5 minutes until the soup is silky, heated through, and slightly thickened.
Use a ladle to serve the hot, velvety soup into bowls. Garnish with fresh herbs if desired, and enjoy the comforting, earthy flavors in every spoonful.
