Start by prepping your ingredients: trim and thinly slice the mushrooms, mince the shallot, and separate the butter into four pieces.
Heat the oil in a saucepan over medium-high heat.
When the oil just starts smoking, add the sliced mushrooms and cook them for about 5m, stirring them occasionally, until they’ve browned and the liquid has evaporated.
Add the shallot, and cook for about 1m, until it begins to soften.
Increase the heat to high and add the red wine and broth. Bring the mixture to a rapid simmer and cook until it is reduced to about 1 cup of liquid (about 5 minutes, for us).
Add the vinegar and mustard and cook for about one minute, until the whole mixture is thickened.
Remove from the heat, and whisk in the butter and thyme. Add salt and pepper, spoon over steaks (or whatever else) and serve immediately.