In a bowl, combine eggless mayonaise, French dressing, sweet pickle relish, apple cider vinegar, and minced onion. Refrigerate for several hours, so that the flavors can meld. There will be plenty of extra. Serve any additional sauce on the side, so that people can drizzle it on their burgers while they eat.

Start by thawing the burgers. Leave them on the counter to thaw or use the thaw function on the microwave. While the buns are still partially frozen, slice a quarter inch off of 2 bottom buns. That will be the middle bun in the Mini Mac.

Slice the cheese down to an appropriate size for the burger. Use one of the buns as a guide against a piece of cheese to know how small to cut it. Set the cheese aside for later.

To grill the burgers, heat outdoor grill to 400 degrees. Grill on each side for 2-3 minutes, until the burgers get nice grill marks. Put the buns on the grill with the cut side down and grill for a couple of minutes until toasty. Remove from grill.

To cook burgers on stove top, put vegetable oil in a warm non-stick skillet. Cook patties for a minute and a half on each side. In last minute of cooking, place buns in pan and cook for 30 seconds on each side.

Assemble the burgers in the following order, starting with the bottom up: bottom bun, a spoonful of special sauce, a pinch of onion, a pinch of lettuce, non-dairy cheese, burger patty, middle bun, a spoonful of special sauce, a pinch of onion, a pinch of lettuce, 2 pickle slices, burger patty, and top bun. Repeat with second sandwich.