Sujebi (Hand-Torn Noodle Soup)

Ingredients

• 180 grams (1½ cups) all-purpose flour, plus more for dusting
• 1 large egg
• 1 teaspoon neutral oil, like vegetable or canola
• 3/4 teaspoon kosher salt, divided
• 1/4 cup lukewarm water, plus more as needed
• 2 scallions, ends trimmed
• 1/4 medium yellow onion
• 1/2 small russet potato
• 1/2 small zucchini
• 1 (16-gram) dried seafood pack
• 1 tablespoon Korean soup soy sauce
• Chile oil or kimchi, for topping (optional)