Pat chicken pieces completely dry and season generously with salt and pepper. Heat 1 tablespoon butter and the olive oil in a large Dutch oven over medium-high heat until shimmering. Add chicken in a single layer and cook undisturbed until golden brown on the bottom, about 4 minutes. Flip and cook 2 minutes more. Transfer to a plate; the chicken will finish cooking later.

Add mushrooms to the same pot and cook over medium-high heat, stirring occasionally, until they release their moisture and turn deep golden brown, about 8 minutes. Push mushrooms to the edges of the pot.

Add remaining 3 tablespoons butter to the center of the pot. Once melted, add onion and cook until softened and translucent, about 4 minutes. Stir in garlic and thyme; cook until fragrant, 30 seconds.

Sprinkle flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste. The mixture will look pasty and coat the vegetables.

Slowly whisk in chicken broth, scraping up any browned bits from the bottom of the pot. Stir in soy sauce and return chicken with any accumulated juices to the pot. Bring to a boil, then reduce heat to maintain a gentle simmer. Cook until chicken is tender and cooked through, about 12 minutes.

Remove from heat and stir in heavy cream. Taste and adjust seasoning with salt and pepper. Ladle into bowls and garnish with fresh thyme leaves. Serve immediately with crusty bread.