Cut chicken breasts into 1-inch pieces. Season with garlic powder, salt, and black pepper, then lightly coat in flour. Heat 2 tablespoons olive oil in a deep skillet over medium-high heat. Add half the chicken pieces without crowding and cook for 3-4 minutes per side until golden brown with a nice crust and internal temperature reaches 165°F. Transfer to a plate. Add more oil if needed and cook remaining chicken.

Reduce heat to medium and add 1 tablespoon each of olive oil and butter to the skillet. Once butter melts, add sliced mushrooms and chopped onion. Cook for 6-8 minutes, stirring occasionally, until mushrooms release their liquid completely and it evaporates, leaving the mushrooms golden-brown and slightly caramelized.

Stir in Dijon mustard, Worcestershire sauce, and minced garlic. Cook for 1 minute, stirring constantly, until fragrant. Pour in chicken broth and scrape up browned bits from bottom of pan with wooden spoon. Return browned chicken to skillet and simmer for 2 minutes.

Reduce heat to low and remove pan from heat for 30 seconds. Stir in room-temperature sour cream until sauce is smooth and creamy. Return to low heat to warm through for 1 minute, but do not let boil. If sauce separates, remove from heat and whisk in 1 tablespoon cold sour cream. Taste and adjust seasoning with salt and pepper as needed before serving.