Make the broth: In a medium saucepan, combine the water, corncobs and kombu over medium heat. Bring to a simmer, then remove from the heat and add the bonito flakes. Let steep for 5 minutes, then strain, discarding the solids. Cool completely, then whisk in the white soy sauce and miso. Refrigerate until chilled, 1 hour.
Prepare the toppings: In a medium skillet, heat the vegetable oil over medium-high heat. Add the corn kernels and sauté until lightly golden, 3 to 4 minutes. Season with salt and let cool.
Bring a small saucepan of water to a boil, add the eggs and cook until soft-boiled, 6 minutes. Transfer to an ice bath to chill before peeling.
Bring a medium saucepan of salted water to a boil. Add the somen noodles and cook until tender, 1 to 2 minutes. Drain in a colander and rinse with cold water to cool. Transfer to a bowl and toss with the hot chile sesame oil.
In each bowl, divide the noodles, corn, tomatoes and spiralized squashes in piles next to each other. Divide the broth between the bowls, then cut each egg in half and nestle on top of the noodles. Garnish with cilantro leaves and squash blossoms, then serve.