In a large bowl, whisk together 370 g all-purpose flour, cake flour, and 3 g salt until well combined. Add boiling water and mix with a wooden spoon until a shaggy dough forms, with no visible wet spots, about 1 minute. Add 160 g room temperature water and mix until dough is cohesive and no dry flour remains.

Using your dominant hand, knead dough in bowl, stabilizing bowl with other hand, until dough begins to clear sides of bowl, about 2 minutes. Transfer dough to counter and continue kneading until dough forms a rough, cohesive ball, about 2 minutes. Invert now-empty bowl to cover dough and let rest for 15 minutes.

Uncover dough and knead until a smooth ball forms, about 15 seconds. Cover dough and let rest for 45 minutes and up to 2 hours.

In a medium heatproof bowl, stir together remaining 120 g all-purpose flour, 100 g scallion whites, remaining 20 g kosher salt, Sichuan peppercorns, and white pepper until well combined.

In a 2-quart saucepan, heat 240 g oil over high heat until oil registers 415 °F / 213 °C on an instant-read thermometer. Carefully pour hot oil over flour mixture and let sit until bubbling subsides, about 20 seconds. Stir in 20 g sesame oil until mixture is well combined and pasty. Set aside.

Uncover dough and divide into 8 equal portions, 120 to 125 g each. Using lightly oiled hands, form each portion into a smooth ball, and re-cover.

Set up a pasta roller at one end of work surface. Dust work surface with flour. Working with one dough portion at a time, keeping the remaining portions covered, use a rolling pin to roll dough into a 5- by 6-inch rectangle, keeping the sides as square as possible.

Using a pasta roller, run dough through the widest setting. Gradually roll the sheet through finer and finer settings, dusting dough liberally with flour as needed to prevent it from sticking to roller. Roll until sheet reaches about 1 mm in thickness and measures 35 to 40 inches long by 6 inches wide.

Arrange sheets parallel to each other on counter. Using a sharp knife, trim 2 to 5 inches from ends of dough sheets to form two 30-inch-long sheets with straight, square edges.

Starting 6 inches from right edge of the sheet farthest from you, lightly brush scallion oil paste over 2 sheets until surfaces are evenly coated. Sprinkle 25 g scallion greens evenly over coated surfaces.

Starting from top sheet with uncoated edge, gently fold 6 inches of uncoated dough over to the left, taking care not to stretch out dough. Continue folding at 6-inch intervals, brushing away excess flour from dough after each fold, until top sheet is completely folded up into a roughly 6-inch square packet.

Place packet on top of left end of second dough sheet and fold dough over, working from left to right this time. Continue folding at 6-inch intervals, brushing away excess flour as you go, until you have a thick, roughly 6-inch square packet. Using the palm of your hand, gently press down on dough to help layers adhere slightly, and form packet into a 6 ½-inch square.

Wrap pancake completely in plastic wrap, transfer to ½ sheet pan, and refrigerate.

Refrigerate pancakes for at least 12 hours and up to 36 hours.

When dough is rested and ready to cook, transfer sheet pan to freezer. If you plan on cooking pancakes as soon as possible, freeze pancakes until slightly firm at the edges, at least 30 minutes and up to 2 hours.

Make the sauce while the pancakes firm up in the freezer. In a small bowl, whisk together soy sauce, vinegar, remaining 15 g water, sugar, remaining 5 g sesame oil, ginger (if using), and chile powder (if using), until sugar is fully dissolved, about 30 seconds. Set aside.

In a 10-inch cast iron or carbon steel skillet, heat 10 g oil over medium heat until shimmering. Work with one pancake at a time while keeping the rest in the freezer. Unwrap pancake, carefully place in pan, cover pan, and cook until bottom side is browned and dough begins to puff slightly, 2 to 3 minutes.

Using a spatula, carefully flip pancake. Cover and continue to cook until second side is lightly browned, 2 to 3 minutes longer.

Uncover skillet, flip pancake, and continue to cook, uncovered, flipping pancake every 2 to 3 minutes, until golden brown and crisp on both sides, 4 to 6 minutes longer. Total cook time ranges from 8 to 12 minutes. Transfer pancake to prepared sheet pan and season with salt to taste.

Transfer pancakes to cutting board. Using a sharp knife, cut each pancake into 4 squares. Serve with dipping sauce.