Spicy Mixed Noodles With Kimchi (Bibim Guksu)

Ingredients

• 1 cup kimchi (see notes)
• 1 tablespoon juice from kimchi (optional)
• 2 tablespoons toasted sesame oil, plus more for drizzling
• 1 teaspoon gochujang (optional)
• 1 teaspoon sugar
• 8 ounces angel hair pasta
• 2-3 ice cubes
• Salt to taste
• 2 mini cucumbers or 1 English cucumber, julienned
• 1 tablespoon toasted sesame seeds
• 1 package (about 0.35 oz) seaweed snacks, cut into thin strips
• 2 Nellie's Free Range Eggs , soft- or hard-boiled