Start by seasoning the chicken thighs with garlic powder, salt, and pepper on both sides. Heat olive oil in a large skillet over medium heat. Place the chicken in the skillet, smooth side down, and press lightly with a spatula. Cook for about 4 minutes until golden, then flip and cook for another 2 minutes. Once done, transfer the chicken to a plate and set it aside.
Increase the heat slightly and melt the butter in the same skillet. Add chopped onions and cook for about 1 minute. Then toss in the sliced mushrooms and sauté them until they turn golden brown. Make sure to scrape up the browned bits stuck to the pan—that's where a lot of the dish’s flavor comes from.
Sprinkle the flour evenly over the onions and mushrooms, stirring it in for about a minute. Gradually add half of the beef broth while stirring to avoid lumps. Then, add the rest of the broth, followed by the Dijon mustard and sour cream. Stir everything together until the sauce becomes smooth and creamy. Lower the heat to a simmer and cook for about 3 minutes until it thickens to a velvety consistency.
Return the chicken (along with any juices on the plate) to the sauce. Simmer everything together for just 1 minute, allowing the flavors to meld beautifully. The chicken will soak up all that incredible sauce, making it irresistibly tender.