Bring a large pot of unsalted water to a boil. Cook egg noodles according to package directions until just tender. Reserve 1/2 cup cooking water, then drain. Time the noodles to finish near the sauce.

Meanwhile melt 1 tablespoon butter in a wide 12-inch skillet over medium-high heat. Add half the mushrooms and cook for 6–8 minutes, stirring occasionally, until their liquid evaporates and edges brown. Transfer to a bowl. Repeat with remaining butter and mushrooms.

Return all mushrooms to the skillet with onion. Reduce heat to medium and cook for 5–7 minutes until onion softens, stirring and adding a tablespoon of measured broth if needed to prevent sticking. Add garlic and cook 30 seconds. Sprinkle flour over the mixture and stir for 1 minute.

Gradually stir in broth, scraping up browned bits. Simmer gently for 5 minutes until lightly thickened. Remove from heat. Stir mustard, salt and pepper into the sauce. Mix a few spoonfuls of warm sauce into the sour cream, then fold that mixture into the skillet. Do not boil after adding sour cream.

Serve the sauce over four portions of noodles, or gently toss together. If necessary, loosen with reserved noodle water a tablespoon at a time. Refrigerate leftovers promptly in shallow containers within 2 hours, or 1 hour above 90°F. Store at 40°F or below for 3–4 days and reheat throughout to 165°F.