Pat the chicken pieces dry with a paper towel. In a medium bowl, combine the flour, paprika, salt, and pepper. Add the chicken pieces and toss until they are evenly coated.

In a large skillet or Dutch oven, heat 2 tablespoons of butter and the olive oil over medium high heat. Once the butter is melted and sizzling, add the chicken in a single layer. Brown the chicken on all sides, about 3 to 4 minutes per side. Remove the chicken from the skillet and set it aside on a plate.

Reduce the heat to medium and add the remaining 2 tablespoons of butter to the same skillet. Add the chopped onion and cook until it begins to soften, about 3 to 4 minutes. Add the sliced mushrooms and a pinch of salt. Continue to cook, stirring occasionally, until the mushrooms have released their moisture and started to turn golden brown, about 5 to 7 minutes. Add the minced garlic and cook for another minute until fragrant.

Sprinkle any remaining flour mixture from the chicken bowl into the skillet and stir it into the vegetables. Cook for about a minute to toast the flour. Slowly pour in the chicken broth, whisking constantly to avoid any lumps. Bring the mixture to a simmer, scraping up any browned bits from the bottom of the pan with a wooden spoon.

Reduce the heat to low. Return the seared chicken and any accumulated juices back into the skillet. Let everything simmer gently for about 8 to 10 minutes, or until the chicken is cooked through and the sauce has thickened slightly.

Remove the skillet from the heat. Stir in the Dijon mustard. Then, gently fold in the room temperature sour cream until the sauce is smooth and creamy.

Taste the sauce and adjust the seasoning with more salt and pepper if needed. Serve immediately over a bed of warm egg noodles. Garnish generously with fresh chopped parsley or dill.