Mix the mustard, brown sugar, thyme, ginger, paprika, and 1 tsp. salt in a small bowl until well combined. Coat both sides of the steaks with the spice mix.
Remove and discard the stems from the shiitakes, if using, and trim the stem ends from the cremini. Wipe all the mushrooms clean and slice them 1/4 inch thick.
Heat the oil in a large skillet over medium-high heat. When the oil is shimmering, add half the steaks and sear them until nicely browned, 2 to 3 minutes per side (the steaks will brown quickly because of the sugar in the spice mix). Transfer to a plate and repeat with the remaining steaks.
Reduce the heat to medium, add 1 Tbs, of the butter to the pan, and let it melt. Add the mushrooms, the scallion whites, and 1/4 tsp. salt and cook, stirring occasionally with a wooden spoon, until the mushrooms soften and brown, 4 to 6 minutes. Pour in the beer and Worcestershire. Scrape the bottom of the pan with the spoon, raise the heat to medium high, bring to a boil, and cook, uncovered, until the liquid is reduced by half, about 4 minutes. Return the steaks and any accumulated juices to the pan, cover tightly with a lid or foil, and reduce the heat to a low simmer. Braise, turning the steaks after 8 minutes, until tender and just cooked through (they should be easy to slice with a paring knife), about 16 minutes total. Transfer the steaks to a cutting board and slice them thinly. Cut the remaining 1 Tbs. butter into four peices and swirl them into the sauce. Stir in the scallion greens and taste for seasoning. Serve the steak slices topped with the sauce.