Spread refried bean mixture on one slice of bread. Top with shredded vegan cheddar. Top with other slice of bread.
Spread 1 teaspoon vegan mayo on the outside of one of the slices of bread. Place face down in a hot pan. While the grilled cheese is cooking over medium heat, spread the other teaspoon of vegan mayo on the other piece of bread (the side facing you). Cook until golden brown on both sides.