Move the oven rack two slots from the top, then heat to 450.
Spread the vegan butter evenly over both English muffin halves. Place on a metal baking sheet then toast in the oven for about 5 minutes, or until starting to lightly brown.
Meanwhile, in a medium bowl mash the chickpeas until mostly smooth, with some little chunks remaining for texture. Stir in the mayo, tamari, lemon juice, pickle, nori, dill, pepper, and salt. Taste and adjust to your liking.
Top the toasted English muffin halves with the chickpea mixture, lightly patting down with a fork. Then, place half a cheese slice on top of each. Bake for 12 minutes, or until hot and melty.
Top both muffins with sliced tomato, avocado, arugula, a squeeze of fresh lemon, plus salt and pepper.