Cut the chicken breast halves into 1-inch pieces. Sprinkle them evenly with garlic powder, salt, and black pepper to taste. Next, coat each chicken piece in flour, ensuring all sides are lightly covered. This will help create a nice crust during cooking.
Heat 2 tablespoons of olive oil in a deep skillet over medium-high heat. When hot, add half of the coated chicken pieces, making sure not to overcrowd the pan. Cook for about 3 minutes on each side until golden brown and cooked through (165°F internal temperature). Flip each piece once for even browning. Transfer the cooked chicken to a plate. For the second batch, add an additional tablespoon of olive oil if the pan is dry, cook the remaining chicken, and transfer it to the plate along with the first batch.
In the same skillet, reduce heat to medium and add 1 tablespoon olive oil and the butter. Once melted, add the sliced cremini mushrooms and chopped onion. Cook for 6-8 minutes, stirring occasionally, until the vegetables release their water, it evaporates, and the mushrooms are nicely seared. This adds rich flavor as a base for the sauce.
Stir in the Dijon mustard, Worcestershire sauce, and minced garlic. Cook for about a minute, stirring constantly, until the mixture is fragrant. I like to sauté the garlic only briefly at this stage to prevent burning while allowing its flavor to permeate the sauce.
Pour in the chicken broth, using a wooden spoon to scrape up any browned bits stuck to the bottom of the pan; these add fantastic depth to the sauce. Return the browned chicken (from Step 2) to the skillet and simmer for about 2 minutes, stirring occasionally, so flavors meld and the chicken warms through.
Reduce the heat to low and stir in the sour cream until the sauce is smooth. Let it heat through for about a minute, but don't allow the mixture to boil to prevent curdling. Taste the sauce and adjust with salt and pepper as needed before serving. For an extra silky texture, I sometimes use full-fat sour cream here, but you can adjust based on preference.