Cook egg noodles in water with the tablespoon salt according to package directions. Reserve 1/2 cup noodle water and drain.
Meanwhile, season chicken with 1/2 teaspoon salt and pepper. Heat oil in a large skillet and cook strips for 6 to 8 minutes until at least 165°F; transfer to a plate.
Add butter, mushrooms and onion to the skillet and cook for 8 to 10 minutes until the mushroom water evaporates. Stir in flour for 1 minute, then gradually add broth, mustard, paprika and remaining salt and simmer for 3 minutes.
Return chicken and remove the skillet from heat. Whisk 1/4 cup warm sauce into the sour cream, then stir that mixture into the skillet.
Fold in noodles and warm over very low heat for 1 minute without boiling, adding reserved noodle water if needed for a spoonable sauce. Serve promptly.