Season the skirt steak with salt and pepper and griddle until medium-rare. Let rest and slice against the grain.
Arrange the 2 pancakes on a work surface, and spread with mayonnaise. Divide the meat between them, then top with cucumbers, pickled peppers, scallions, mint, cilantro and a drizzle of chili oil. Roll up tightly and slice.
For the roux: Melt the butter in a medium saucepan over medium heat, then whisk in the flour, salt and sesame oil. Cook, whisking constantly, until light amber in color, 5 to 7 minutes.
For the first dough: Mix the flour and boiling water together in a small bowl until a dough forms. Knead for a minute or two to make sure that everything comes together. Set aside.
For the second dough: Meanwhile, pour the room temperature water into the bowl of a stand mixer and top with flour and salt. Mix with the dough hook on medium-low speed until dough starts to come together. While dough is in the beginning phase of mixing, add in the hot water dough in small chunks. Knead on medium-low speed until the dough comes together and leaves the sides of the bowl. Turn out onto a work surface (oiled so the dough does not stick) and knead by hand until smooth and one consistent temperature; be careful not to overwork. Wrap tightly in plastic and let rest at room temperature for at least 30 minutes.
For rolling out: Divide dough into 65-gram portions and cover with plastic wrap. (The dough dries out very quickly before it is rolled out, so be sure to keep it covered if you are not working with it.) Squeeze a tablespoon or so of oil onto a very clean marble, stone or metal countertop and spread around. Place one dough ball in the center of the oiled surface. Gently but using force, roll dough ball with a floured rolling pin until very thin and slightly translucent. The rolled dough will be oddly shaped and that is okay. If the dough rips, that's also ok--it's still usable. Once dough is rolled to translucent point, brush with a layer of roux and sprinkle with 2 tablespoons of sliced scallions.
Working from the bottom end of the rolled dough (the end closest to your body), begin gently rolling dough up like a cigar. The end result will be a long "snake". Twist the snake into a coil. Smash the coil down with your palm and roll this into a 10-inch-wide pancake. Repeat until all your pancakes are complete. Store the pancakes in the refrigerator between layers of parchment paper greased with oil until you're ready to cook.
Heat a pan over medium-low heat. Add a small amount of oil and a cold pancake to the pan. Cover with a lid and cook until light golden brown, 4 to 5 minutes, before flipping and covering again. Cook the other side until golden brown, another 4 to 5 minutes. Remove to a plate. Serve hot.