Melt butter in a 2.5 quart sauce pot (or larger). Add diced onions and mushrooms to the butter, season with salt and pepper, and sauté for about 6-8 minutes until tender. Add garlic and sauté for about a minute until fragrant.
Add ground beef to the pot, break it up with a spoon, and cook until it's cooked through and no longer pink.
Sprinkle flour and dried thyme over the veggies, mix to coat, and cook for 2 minutes.
Add beef broth, Dijon mustard and Worcestershire sauce to the pot and stir to combine. Bring the broth to a boil over medium heat. Add egg noodles and cook for about 7 minutes, until they are almost tender (al dente).
Add half and half and stir to combine. Bring back to boil and cook for about a minute to thicken the sauce. Remove from heat (sauce will continue to thicken a bit) top with fresh chives, and serve.