Mix all the ingredients together in a bowl. The mixture should hold together when formed into a cake. If it doesn't, add some more breadcrumbs and mayonnaise. (Update: a couple of people who tried these said they had trouble getting the crabcakes to hold together. I'd advise pulsing a few times in a food processor. Also these are delicate so don't make them too big. Mine were just over an inch in diameter. Be gentle when you flip them over.)
In a non-stick or cast-iron skillet, heat the oil
Take about a 1-inch ball of the batter and flatten it slightly.
Place as many cakes as possible into the skillet without overcrowding them. If you put too many in, they will steam and turn soggy instead of getting that beautiful golden-brown crust.
Turn after 1-2 minutes, once the underside is thoroughly browned. Cook the other side.
Serve hot, either by themselves or in a chapati or tortilla wrap smeared with some more mayonnaise. You can also add tomatoes or other veggies like cucumber or lettuce.