Place corned beef along with the contents of spice packet into a pot, and cover by 2 inches with water. Bring to a boil, reduce heat to low, and simmer for 2 hours 15 minutes. While corned beef is cooking, occasionally add more water to keep the level near where it was when it started boiling.

Remove corned beef to a bowl, and let cool until cool enough to handle, at least 30 minutes. Reserve 1 cup cooking liquid.

When meat is cool, slice off most of the fat. Cut meat with the grain into thick strips, and then turn and slice into thin, bite-sized pieces. Reserve until needed.

Heat oil in a pan over medium-high heat. Add mushrooms and salt to the hot pan, and cook and stir until mushrooms are nicely browned, about 3 minutes. Add onions, and continue cooking until they soften and turn translucent, about 3 minutes. Add butter and stir until melted.

Make a space in the center of the pan, add garlic, and sauté until fragrant, about 30 seconds. Add flour, and cook and stir for 1 minute more. Pour in white wine and reserved corned beef cooking liquid, and stir to combine. Raise the heat to high, bring to a boil, and cook, stirring, until sauce reduces by about half and thickens, 3 to 5 minutes more.

Stir in beef broth, and continue to boil and reduce until sauce thickens again, 6 to 7 minutes. Stir in crème fraiche, and reduce until the sauce is as thick as you’d like, a few more minutes.

Stir in sliced corned beef, and reduce heat to medium-low. Cook, stirring occasionally, until meat is heated through, 2 to 4 minutes. Sprinkle with fresh dill.

Garnish each serving with a small dollop of crème fraiche or sour cream and a little fresh dill.