Combine all the sauce ingredients together in a bowl and refrigerate until ready to assemble the vegan "big mac".
Cook vegan burger patties in a pan on the stove or on a barbecue, and baste them in barbecue sauce as you go. Melt vegan cheddar cheese slices on top during last minute of cooking.
Cut one kaiser roll in half. Take another kaiser roll and cut a slice off the bottom for the middle piece of the burger.
Put vegan "big mac" sauce and relish (if using) on both the bottom and middle pieces of the bun, and the inside of the top of the bun. Add your burger patties with vegan cheddar cheese between each piece of bun, and then add onions, lettuce, and pickles to your liking.