Season both sides of the chicken with garlic powder, salt, and pepper. Heat olive oil in a large skillet over medium heat, then place the chicken smooth side down. Press gently with a spatula and cook for 4 minutes until golden brown. Flip the chicken, press lightly again, and cook for an additional 2 minutes. Transfer the chicken to a plate and set aside.
Increase the skillet heat to medium-high and melt the butter. Add the onions and sauté for 1 minute, followed by the mushrooms. Cook until the mushrooms turn golden, scraping the pan to lift the browned bits for added flavor.
Sprinkle the flour over the mushrooms and stir continuously for 1 minute. Gradually pour in half the beef broth while stirring, ensuring the flour is incorporated, then add the remaining broth.
Mix in the Dijon mustard and sour cream, stirring until the sauce is smooth. If it appears slightly split, don’t worry; the sour cream will blend as it heats. Bring the sauce to a gentle simmer, then reduce the heat to medium-low and cook for approximately 3 minutes until it thickens to a pourable consistency. Adjust salt and pepper to taste.
Return the chicken and its plate juices to the skillet, simmering for 1 minute to warm through. Remove the skillet from heat.
Serve the chicken stroganoff over your choice of pasta or egg noodles, garnished with parsley or chives if desired.