Make tomato broth. In a food processor or high powered blender, add chopped tomatoes, garlic, soy sauce, mirin, sugar, vinegar, instant dashi powder and water. Puree until smooth and well combined. It should just measure 4 cups. Transfer to a 4-cup measuring cup and stir in the chopped green onion. Cover and chill in the fridge.
Cook noodles and eggs. To a medium pot of water, carefully add eggs (if using). Bring to a boil. When the water is boiling, add the somyeon and stir briefly to make sure the noodles don't clump together. Cook until al dente, about 3-4 minutes.
TIP: About halfway through the cooking process, the water will foam and bubble up. Add 1 cup cold water and let it come up to a boil again. (This process results in a chewier noodle).
Set up cold water bath. While the noodles cook, make a cold water bath: to a medium bowl, add cold water and ice cubes. Set aside.
Drain noodles. When the noodles are al dente, transfer both the noodles and eggs to a colander to drain the water. Transfer the eggs to the water bath. Rinse the noodles with cold water until cool to the touch. Set aside to drain.
Assemble bowl. Divide Somyeon evenly between two bowls. Divide the tomato broth and add to the two bowls. Make sure not to pour the tomato broth on top of the noodles but around the sides, so the noodles mound up in the middle. Add a few ice cubes to the tomato broth.
Garnish. To each bowl, add a drizzle of sesame oil and a sprinkle of sesame seeds. Add finely julienned perilla leaves on top.
Serve. Serve immediately and enjoy!