Put the skirt steak into a 1-gallon resealable plastic bag. Whisk together the garlic, soy sauce, brown sugar, rice wine vinegar, ginger, sesame oil, chili flakes and scallion whites in a small bowl. Pour two-thirds of the marinade over the steak, reserving the remaining marinade. Seal the bag, removing as much air as possible. Set aside and let marinate for at least 10 minutes.
Meanwhile, whisk together the mayonnaise and sriracha in another small bowl.
Heat 2 tablespoons each of olive oil and butter in a large cast iron skillet over medium-high heat. Remove the steak from the marinade and sear on each side until cooked to the desired temperature, 3 to 4 minutes per side for medium rare. Remove the steak to a cutting board to rest while you cook the vegetables.
Add the remaining 1 tablespoon olive oil and 1/2 tablespoon butter to the skillet. Add the bok choy, cut side-down, and sprinkle the mushrooms around the skillet. Allow to brown and cook for 2 to 3 minutes. Flip the bok choy, whisk the reserved marinade to combine and pour into the skillet and let reduce slightly. Remove from the heat.
Slice the steak against the grain. Transfer the bok choy to a platter with any sauce that is in the skillet, top with the shiitake mushrooms, arrange the sliced steak along the edges, and garnish with the reserved scallion greens. Serve with the sriracha mayo.