How to Make It
In a medium bowl, whisk the kimchi juice with 3 tablespoons of the rice wine vinegar, the Asian fish sauce and 1 1/2 cups of water. Season with salt. Cover and freeze, stirring with a fork and scraping the frozen edges into the center a few times, until slushy, about 1 hour and 30 minutes.
Meanwhile, in a pot of boiling water, blanch the corn until crisp-tender and bright yellow, about 2 minutes. Drain the corn and cool under cold running water, then cut the kernels off the cobs and transfer to a small bowl. Season the corn with salt, cover and refrigerate.
Return the water to a boil. Add the ramen and cook until al dente. Drain and cool under cold running water, then drain again and transfer to a large bowl. Add the remaining 1 teaspoon of vinegar and the toasted sesame oil. Season with salt and toss to coat.
Stir the partially frozen broth, then transfer to bowls. Top with the ramen, corn, chopped kimchi, scallions, mushrooms and cucumber and serve.