Instructions

1. Prepare the following, placing each ingredient into a separate pile on a baking sheet as you complete it: Trim the stems from 1 pound fresh shiitake mushrooms and cut into 1/4-inch-thick slices (about 6 cups); peel and cut 3 medium carrots into matchsticks (about 2 cups); cut 3 Korean or zucchini squash into matchsticks (about 3 cups); peel and cut 1 pound Korean or daikon radish crosswise into thin rounds, then stack them together and cut into matchsticks (about 4 cups).
2. Bring a large saucepan filled three-quarters full with water to a boil over medium-high heat. Add 1 teaspoon of the kosher salt and 1 pound spinach in 2 batches. Cook, stirring occasionally, until wilted, about 2 minutes.
3. Drain the spinach. When cool enough to handle, grab handfuls of the spinach, squeeze out as much water as possible, and place in a small bowl. Finely grate 1 of the garlic cloves on a Microplane onto the spinach. Season with 1/2 teaspoon of the kosher salt and drizzle with 1 tablespoon of the toasted sesame oil. Mix with your hands until combined.
4. Fill the now-empty saucepan three-quarters full with water and bring to a boil over medium-high heat. Add 1 teaspoon of the kosher salt and 12 ounces soybean sprouts. Cover and simmer, reducing the heat as needed, for 20 minutes. Meanwhile, cook the remaining vegetables.
5. Heat 1 tablespoon of the neutral oil in a large nonstick frying pan or cast iron skillet over medium-high heat until shimmering. Add the carrots and 1/2 teaspoon of the kosher salt. Stir-fry until brighter in color and crisp-tender, 2 to 3 minutes. Return to the baking sheet. Wipe out the pan with paper towels.
6. Heat 1 tablespoon of the neutral oil in the same pan over medium-high heat until shimmering. Add the squash and 1/2 teaspoon of the kosher salt. Stir-fry until crisp-tender, 2 to 3 minutes. Return to the baking sheet. Wipe out the pan with paper towels.
7. Heat 1 tablespoon of the neutral oil in the same pan over high heat until shimmering. Add the mushrooms, 1 tablespoon soy sauce, and 1 teaspoon of the toasted sesame oil. Finely grate 1 of the garlic cloves over the mushrooms. Stir-fry until the mushrooms are charred in spots, 4 to 5 minutes. Return to the baking sheet. Wipe out the pan with paper towels.
8. Heat 1 tablespoon of the neutral oil over medium-high heat until shimmering. Add the radish, 1/2 teaspoon of the kosher salt, and 1/3 cup water. Cook, stirring occasionally, until the radish is translucent and tender but not browned, 8 to 10 minutes. When the radish is almost ready, add 1 tablespoon of the toasted sesame oil and stir-fry for 1 minute more. Return to the baking sheet and reserve the frying pan.
9. When the soybean sprouts are ready, drain and transfer to a medium bowl. (See recipe note for usages for cooking liquid). Finely grate the remaining garlic clove over the sprouts. Season with the remaining 1/2 teaspoon kosher salt and drizzle with 1 tablespoon of the toasted sesame oil. Mix with your hands until combined.
10. Place 3 tablespoons of gochujang, the remaining 2 tablespoons toasted sesame oil, 2 tablespoons mirin, and 1 tablespoon honey in a small bowl and whisk to combine.
11. Wipe out the reserved frying pan with a paper towel. Heat the remaining 1 tablespoon neutral oil in the pan over medium heat until shimmering. Swirl the pan to coat the bottom with the oil. Crack 4 to 6 large eggs into the pan, spacing them evenly apart. Reduce the heat to low. Cover and cook undisturbed until the whites are set and the yolks are still runny, 2 1/2 to 3 1/2 minutes.
12. While the eggs are cooking, start to assemble the bibimbap. For each serving, place 1 cup hot cooked rice in a bowl. Divide and arrange the spinach, mushrooms, carrots, squash, sprouts, and radish in separate piles on the rice.
13. Top each bowl with a fried egg and sprinkle with toasted sesame seeds. Drizzle each bowl with 1 to 2 tablespoons of the gochujang sauce and serve any remaining sauce on the side.