Korean Rice Bowl (Dolsot Bibimbap)

Ingredients

• 1 cup cider vinegar
• 2 tablespoons sugar
• 1 1/2 teaspoons salt
• 1 cucumber, peeled, quartered lengthwise, seeded, and sliced thin on bias
• 4 ounces (2 cups) bean sprouts
• 1/4 cup gochujang
• 3 tablespoons water
• 2 tablespoons toasted sesame oil
• 1 teaspoon sugar
• 2 1/2 cups short-grain white rice
• 2 1/2 cups water
• 3/4 teaspoon salt
• 1/2 cup water
• 3 scallions, minced
• 3 tablespoons soy sauce
• 3 garlic cloves, minced
• 1 tablespoon sugar
• 1 tablespoon vegetable oil
• 3 carrots, peeled and shredded (2 cups)
• 8 ounces shiitake mushrooms, stemmed, caps sliced thin
• 1 (10-ounce) bag curly-leaf spinach, stemmed and chopped coarse
• 2 tablespoons plus 2 teaspoons vegetable oil
• 1 tablespoon toasted sesame oil
• 4 large eggs