Stir together flour, salt, and 3/4 cup plus 1 tbsp. boiling water in a bowl until a shaggy mass forms. Turn out onto a floured work surface and knead until smooth and elastic, 3 to 5 minutes. Wrap in plastic wrap and let rest 30 minutes.
Meanwhile, heat 1 tbsp. vegetable oil in a large nonstick frying pan over medium heat. Cook green garlic, stirring often, until softened and starting to brown, 4 to 5 minutes.
Combine soy sauce, vinegar, chili garlic sauce, and 1 tsp. sesame oil in a small bowl; set dipping sauce aside.
Divide reserved dough into 4 equal pieces and pat each into a disk. Roll each into a very thin circle about 12 in. wide, using just enough flour on the work surface to prevent sticking. In a bowl, mix 1 tbsp. vegetable oil with remaining 2 tsp. sesame oil. Lightly brush dough circles with oil mixture. Sprinkle one-quarter of cooked green garlic over each piece of dough.
Roll up each garlic-sprinkled dough circle like a cigar. Starting with one end, coil tube into a spiral so it looks like a cinnamon roll and press outer end into spiral to seal. Sprinkle each spiral with flour and carefully roll out into a flat disk about 6 in. wide (some garlic may poke through).
Heat 2 tsp. vegetable oil in the nonstick frying pan over medium heat (use 2 pans if you have them). Cook pancakes one at a time, adding oil for each batch and turning pancakes once or twice, until deep golden brown and crisp, about 8 minutes per side.
Cool pancakes slightly before cutting into wedges. Serve with dipping sauce.
Tips for cooks
Green garlic is simply immature regular garlic and tastes fresher and more delicate. It has juicy, edible stalks with no bulbs at the base (if picked quite young), or bulbs with tiny cloves that don't need peeling.
FIND Look for slender pale green stalks in springtime at farmers' markets and some supermarkets. Or substitute green onions plus regular garlic (see the recipe).
PREP Trim green garlic as you would green onions, removing tough tops (save to flavor soup) and roots, plus any tough outer layers. Ten stalks yield 2 cups chopped.
*If you can't find green garlic, use 2 cups chopped green onions plus 6 minced garlic cloves.