Step 1Bring a large pot of water to a boil. While waiting, put the tomatoes in a large bowl, generously season with salt, toss, and let stand.
Step 2Once the water boils, boil the eggs: Add as many eggs in their shells as you plan to serve. Boil for 4 minutes. Use a slotted spoon to transfer to a small bowl and cover with ice and water.
Step 3Generously salt the boiling water and add the noodles. Cook according to the package directions. Drain in a colander and rinse under cold water until room temperature. Shake the colander to remove excess water and dump the noodles into the bowl with the tomatoes.
Step 4Cut the kimchi into bite-size pieces if needed. Add the sesame oil and the kimchi with 2 tablespoons of its juices. Toss until well-mixed. Taste and add more oil, juices and salt to taste. Divide among serving dishes. Carefully peel the eggs and add to the bowls, along with more kimchi if you’d like. Cut the eggs in half, roughly hacking at them with your fork or chopsticks, and mixing them with the noodles to coat them with the yolk. Eat immediately.