Udon Nudelsoppa (Kake Udon)

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1. 1
   Stir 2 Tbsp. Diamond Crystal or 1 Tbsp. plus ½ tsp. Morton kosher salt into ¾ cup plus 2 Tbsp. (198 g) water in a small bowl until dissolved. Place 3¼ cups (406 g) all-purpose flour in a large bowl and drizzle salt water evenly over. Stir with a spoon or chopsticks until water is absorbed and shaggy clumps form. Knead dough firmly in bowl until a tight, mostly smooth dough forms, 8–10 minutes (there may be some dry bits but there shouldn’t be any large patches of dry flour). Form dough into a ball and place inside a 2-gal. resealable plastic bag (or, split dough in half and place each in a 1-gal. resealable plastic bag). Seal bag, pressing out excess air and let rest 30 minutes.
2. 2
   Place bag with dough between 2 kitchen towels and place on the floor. Using your heels, step on dough to flatten into a thin disk (hold on to the counter so you don’t slip). Open bag and fold dough into quarters, like a piece of paper. Seal bag, pressing out air, and place back between kitchen towels. Step on dough until flat. Repeat process of folding and stepping 3 more times (5 total). The dough will feel noticeably softer at the end. Seal bag tightly and let dough rest at least 2 hours and up to 12 hours. (If storing longer than 2 hours, chill and bring to room temperature before using).
3. 3
   Flatten dough on a surface to ½" thick. Roll dough out to a 12x10" rectangle about ⅛" thick. For the most even noodles, trim the edges of the dough to make a neat rectangle.
4. 4
   Lightly dust dough with potato starch or cornstarch and fold in half. Using a sharp knife or a bench scraper, cut dough into ⅛"-wide noodles. Shake noodles to detangle, dusting with more potato starch as needed to prevent sticking (try to use less rather than more starch here).
5. 5
   Cook noodles in a large pot of boiling water (no need to salt) until al dente, 8–10 minutes. Drain and rinse under cold running water to remove excess starch and make noodles bouncy.
6. 6
   While the noodles are cooking, bring 4¼ cups water to a boil in a medium saucepan. Add 2 dashi stock powder packets, cover pan, and simmer 2 minutes to release flavors. Remove packet and discard. Add 3 Tbsp. soy sauce, 2 Tbsp. mirin (sweet Japanese rice wine), 2 tsp. sugar, and ¼ tsp. kosher salt to dashi and simmer until sugar and salt are dissolved, about 2 minutes.
7. 7
   Divide noodles among bowls and pour about 1 cup broth over each one. Top each with a pile of one quarter of 4 scallions, thinly sliced, and a large pinch of shichimi togarashi.