Make salad: In a medium bowl, combine kale and fennel. Whisk remaining ingredients together in a small bowl. Toss with salad and let stand 45 minutes to 1 hour, stirring a couple of times, before serving.
Cook steak: In a spice grinder or clean coffee grinder, pulse peppercorns until coarsely ground. Season steaks with 1/2 tsp. salt and rub all over with Sichuan pepper. Let come to room temperature, about 30 minutes. Meanwhile, preheat oven to 400°.
Heat a medium ovenproof frying pan (preferably cast iron) over medium-high heat until hot but not smoking. Swirl in 2 tbsp. oil. Add steak and sear, turning once, until browned on both sides, about 1 minute per side. Slide pan into oven and cook until medium-rare (135° on an instant-read thermometer), 12 to 15 minutes. Transfer steaks to warm plates.
Roast mushrooms: Split maitake into 2 or 3 small clusters (if using shiitake, remove tough stems and thinly slice mushrooms). Set frying pan with steak drippings over high heat. Add mushrooms and season with remaining 1/2 tsp. salt and black pepper to taste. Cook, gently turning once or twice, until wilted and browned, 3 to 4 minutes. Add butter and immediately transfer pan to oven. Cook mushrooms 3 minutes (it's okay if they get quite crisp), then return to stovetop over medium heat. Pour in vinegar, then spoon vinegar-butter mixture over mushrooms a few times.
Serve steak on warmed plates, with mushrooms and salad.
*Find Sichuan peppercorns in your grocery store's spice aisle.
Wine pairing: A powerful, spicy red like Sol Rouge 2012 Petite Sirah (Lake County; $32). The peppery black fruit hugs the beef. --Sara Schneider