Combine flour, salt, and water in a bowl. Mix with a wooden spoon until dough comes together in a sticky ball. Sprinkle in more flour and knead by hand, adding more flour as needed, until soft and supple. Wrap in plastic and let rest at room temperature for 1 hour.

Combine ground pork, garlic, ginger, green onions, and chives in bowl. Season with salt, pepper, gochugaru, soy sauce, and sesame oil. Mix together using two forks just until combined. Cover with plastic wrap and refrigerate until ready to use.

Mix vinegar, soy sauce, and gochugaru into the chicken broth and set aside.

Divide dough into 4 pieces. Roll one piece into a rope about the thickness of your thumb. Using a rolling pin, flatten into a long, thin band about 3 inches wide, flouring only as needed. Dust the top with flour and flip over. Dip your fingers in some water and lightly brush the surface until slightly sticky.

Use moistened fingers to line about 1/4 of the pork filling across the dough. Fold dough over the whole length, pressing it down over the meat. Trim off excess dough if desired. Dust a little more flour on top and roll over so seam side is on the bottom. Divide into 16 pieces using the edge of your hand, then a bench scraper to cut. Repeat with remaining dough and filling.

Heat oil in a pan over high heat. Cook dumplings in batches, seam-side up, until golden brown, 1 to 2 minutes per side. Pour in a portion of the broth and bring to a boil. Cover and continue to boil until pork is no longer pink, about 3 minutes. Pour dumplings with broth into serving bowls.