Bring a large pot of water to a boil then season with a ~1 Tablespoon salt. Place a lid on top then turn the heat down to low to keep warm.
Meanwhile, heat a large, 12+” skillet over medium-heat high. Add the ground beef and shallots/onions then season with salt and pepper and brown, breaking the beef up as it cooks. Drain the beef if necessary then return it to the skillet. Add the worcestershire sauce then cook until the beef absorbs the sauce, 1 minute. Scrape the seasoned ground beef into a bowl, leaving any browned bits in the bottom of the skillet. Set the beef aside.
Return the skillet over medium-high heat then melt the butter inside. Once melted, add the sliced mushrooms then saute until the mushrooms release their liquid and the liquid cooks off, 8-10 minutes, stirring occasionally and turning the heat up slightly to help cook the excess liquid off.
Around the time the mushrooms start releasing their liquid, turn the heat under the pot of water back up to high. Once boiling, add the pasta then cook until al dente. Drain then set aside.
After all the liquid from mushrooms has cooked off, turn the heat back down to medium-high then season the mushrooms with salt and pepper. Continue to saute until golden-brown, 3-4 minutes, then add the garlic and dried thyme and saute until the garlic is very fragrant, 1 minute.
Sprinkle the gluten free flour over the mushrooms then stir to coat and cook while stirring for 1 minute. Switch to a whisk then slowly pour the beef broth into the skillet while whisking to create a smooth sauce with no lumps. Add the milk and Dijon mustard then whisk until smooth.
Switch back to a spatula then bring the sauce to a simmer while stirring. Once simmering, turn the heat down to medium-low then simmer gently until the sauce has slightly thickened, 1-2 minutes. The sauce will thicken slightly as it sits. Tip: the sauce can become grainy if the milk is boiled or simmered too hard, so be sure to keep the sauce at a gentle simmer.
Add the cooked ground beef then stir to combine and heat through. Turn the heat off under the skillet then let the mixture sit and cool for 2 minutes. Add the sour cream then stir until smooth. Scoop the mixture over the cooked egg noodles then serve.