Cut the chicken breasts into uniform 1-inch pieces and pat them completely dry with paper towels. Season the chicken with garlic powder, salt, and black pepper. Place the flour in a shallow dish and toss the chicken pieces in the flour until evenly coated, shaking off any excess.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until shimmering. Working in batches to avoid crowding, add the floured chicken pieces in a single layer. Cook for about 3 minutes per side until golden brown and cooked through to 165°F. Remove the chicken to a plate and set aside.

Reduce heat to medium and add the remaining 1 tablespoon of olive oil and the butter to the same skillet. Once the butter is melted and foaming, add the sliced mushrooms and chopped onion. Cook for 6 to 8 minutes, stirring occasionally, until the mushrooms are deeply browned and the onions are soft and translucent.

Stir in the Dijon mustard, Worcestershire sauce, and minced garlic. Cook for about 1 minute, stirring constantly, until the garlic becomes fragrant and everything is well combined.

Pour in the chicken broth and use a wooden spoon to scrape up all the browned bits stuck to the bottom of the pan. Return the chicken and any accumulated juices from the plate to the skillet. Let everything simmer together for about 2 minutes.

Reduce heat to low. Stir in the room-temperature sour cream, mixing until the sauce is completely smooth and creamy. Let it warm through for about 1 minute, stirring gently, but do not let it come to a boil.

Taste and adjust seasoning with additional salt and pepper if needed. Serve hot over wide egg noodles, rice, or mashed potatoes.