To make the kombu dashi, soak a 2X3 kombu in ¼ cup of water for 30-45 minutes until the kombu turns soft. Drain the kombu dashi into a bowl and reserve the kombu for a side dish. Alternatively, mix 1-2 teaspoon of vegan kombu dashi powder in ¼ cup of water until well combined.
To mash the tofu, place a slab of tofu on a chopping board. Using a pastry scraper or the back of the cleaver, press down ⅓ of the tofu with pressure. Using a pulling motion, drag that portion away while pressing it down to squeeze out the water. Repeat 3-4 times for a whole slab of tofu. Alternatively, place tofu in a nut milk bag and squeeze out the liquid. Transfer tofu to a large bowl. Please note that you'll want a somewhat dry paste as wet paste will break the nori sheet.
Next, place potato cubes in a high-speed blender and blend into a fine paste. Transfer the paste into a nut milk bag and squeeze out the liquid. Then, empty it into the tofu bowl.
Season with salt and pepper. For a darker color, you may use 1-2 teaspoons of soy sauce instead of salt. Add a tablespoon of cornstarch and mix until well combined. Use more cornstarch if needed but don't go over 2 tablespoons. Divide it into 4 equal portions.
Now, make the cornstarch paste by mixing a tablespoon of cornstarch with 1 tablespoon of water.
To assemble, lay a piece of nori on a chopping board, shiny side down. Brush surface with a thin layer of cornstarch slurry. Top it with a portion of the tofu mixture. Using your fingers, spread to cover the nori leaving a 1cm border. Repeat until you are done with all the nori.
Next, heat a nonstick skillet with 2 teaspoons of oil. Place the unagi, tofu side down and pan-fry over med-low heat for 3-4 minutes or until golden brown. To check if it's ready to flip, gently touch the nori side. If it's warm that means the tofu has cooked through. Pan-fry for another minute if you want a crispier tofu side.
Flip and cook the nori side for about 30 seconds. Remove and let it cool completely before cutting.
Using the same skillet, add kombu dashi, soy sauce, mirin, maple syrup, sugar, and bring the mixture to boil. Stir continuously until the sugar has dissolved. Then, turn down the heat to medium and cook down the sauce until you see large bubbles. Turn off the heat and spoon this sauce over the cut unagi.
Garnish the unagi with toasted sesame seeds and chopped green onions. Serve warm with rice or noodles.