Preheat the oven to 200 degrees F.
Trim off any excess fat from the short ribs. In a large saucepan or flameproof casserole, combine 3 quarts of water, the black, white, and Szechuan peppercorns, bay leaves, and thyme. Bring to a boil over high heat. Add the short ribs and partially cover the pot. Reduce the heat to low. Simmer the ribs, skimming off any foam from the surface, until the meat is almost tender when pierced with the tip of a sharp knife, about 1 1/2 hours. Do not overcook, because the ribs will cook further in 2 later steps. Remove the ribs from the braising liquid and let cool to room temperature.
Bring the Shanton Broth and red miso to a boil in a large saucepan over high heat, whisking to dissolve the miso. Add the short ribs and reduce the heat to low. Simmer uncovered, turning occasionally, until the ribs are very tender but not falling apart, about 1 1/2 hours. Using a slotted spoon, transfer the short ribs to a plate and let cool completely. Then remove the meat from the bones, trying to keep each rib in 1 chunk.
While the ribs are cooling, skim off as much fat as you can from the Shanton-Miso broth. Boil over high heat until the liquid is reduced to 1 cup, about 20 minutes. Strain the sauce and set aside. (The short ribs and sauce can be prepared up to 1 day ahead, separately cooled, covered, and refrigerated. Remove from the refrigerator at least 1 hour before deep-frying.)
Heat the oil in a deep-fryer or pour vegetable oil into a large saucepan to reach halfway up the sides. Heat over high heat to 350 degrees F.
Working with half of the short ribs at a time, coat the ribs with the all-purpose flour, shaking off any excess. Dip in the tempura batter and let extra batter drip back into the bowl. Add the coated ribs to the hot oil and deep-fry until light golden brown, about 2 minutes. Using a slotted skimmer, transfer to a wire rack set on a baking sheet to drain. Keep warm in the low oven while frying the remaining short ribs.
To serve, spoon equal amounts of the sauce onto 4 dinner plates. Top each with 2 pieces of Short Rib Tempura and serve immediately.
In a medium bowl, beat the egg yolk with a fork. Whisk in the vegetable oil until blended and then the club soda. Add the flour and stir with chopsticks until just barely combined. Don't worry if some flour floats on top.