Combine all of the brine ingredients in a saucepan. Bring to a rolling boil, then reduce the heat and simmer, covered, for about 10 minutes.
Arrange the tofu in a shallow dish, and pour the hot brine over it. Leave the tofu to marinate for at least 30 minutes, but if you can wait an hour, even better!
Bake at 350° F for 25-35 minutes on a baking sheet lined with parchment paper, until it reaches your preferred texture.
Make the not-a-Reuben sandwich
Divide the mayo between your pieces of bread, and spread it on. Layer on the corned tofu, the kimchi, and the avocado. You can serve the sandwich cold or warm it up in a sandwich press.
Video
Notes
If you don't want to use tofu for the meat, use an equivalent amount of sliced seitan. Instead of baking, pan fry until crispy on the edges.