Season short ribs with salt and oil. Place seasoned meat in a hot braising pan and sear both sides to golden brown, about 3 minutes per side. Remove meat from pan and set aside. Add onions, tomatoes, garlic and mushrooms to pan and continue cooking until caramelized, stirring occasionally. Add short ribs back to pan and add remaining ingredients, except the chicken broth. Add chicken broth to cover short ribs. Cover pan with lid or plastic wrap and foil. Place in a preheated 300°F oven and braise for three to four hours, or until fork tender. Carefully remove short ribs from the braising liquid and set aside. With an immersion blender, puree vegetables until smooth. Simmer to liquid and reduce to a sauce-like consistency. While sauce is simmering, pull the short ribs into shreds. Pour sauce over shredded short ribs and allow to cool.
Combine the all-purpose and bread flours in a standing mixing bowl with a dough hook. Turn on mixer to blend flours. Boil water, turn off heat, and cool for 3 minutes. Turn on mixer and slowly pour water into the flour, stopping occasionally to allow water to absorb into flour. Dough will come together quickly. Turn dough onto a lightly floured cutting board and knead until soft and pliable. Form dough into 20 to 24 4-ounce balls, cover with plastic wrap, and allow to rest for a minimum of 1 hour. When dough is rested, press one dough ball into a flat disk and start forming into a long rectangle. Roll dough with a rolling pin into as thin a rectangle as possible, using flour as needed to keep it from sticking to countertop. Brush dough lightly with Kikkoman Preservative-Free Non-GMO Toasted Sesame Oil and sprinkle liberally with scallions. Starting with the edge of the dough closest to you, start rolling dough into a long rope or snakelike shape. The rope should be as tight as possible. Coil rope into a circle or spiral, cover and allow to rest while you repeat the process with the remaining dough balls. Starting with first coil, roll dough into a very thin round circle to whatever diameter you desire. Grease a very large nonstick skillet or flat-top griddle liberally with peanut oil, cook dough on both sides until lightly golden. This can be done a couple of hours in advance.
Lime Ponzu Vinaigrette:
In a small bowl, add all ingredients and whisk to combine.
In a medium bowl, combine all the salad ingredients and toss together. Take a handful as needed from the bowl, put into a small bowl and drizzle with the vinaigrette and toss.
Spread braising liquid over a scallion pancakes. In the center of the scallion pancakes, scoop a few ounces of pulled short rib meat. Top the short ribs with a generous amount of the salad. Top with a second scallion pancakes. Cut the stack into wedges and top with another handful of the salad.