To make the marinade, roughly chop green onions, cilantro, ginger, garlic and chiles in food processor with metal blade in place. Scrape mixture into large plastic container. Add remaining marinade ingredients and stir to combine.
To marinate meat, cut beef into 1-inch cubes. Add to marinade, cover and refrigerate overnight.
For each serving, split baguette and butter both halves. Grill or toast until lightly browned. Sautee ½ cup sliced mushrooms in butter until lightly browned. Set aside.
Remove 6 ounces beef from marinade and pat dry with paper towels. Sear a la plancha or in a well heated, lightly oiled cast iron skillet. Place 2 ounces cheese over steak cubes; cover and allow to melt. Lift beef and cheese from pan and place on prepared baguette. Top with mushrooms and ¼ cup peppers to serve.