For the aioli: In a small bowl, combine all the ingredients and stir well.
For the BLT: Lay 4 slices of bread on a cutting board. Spread 1 teaspoon or so of the aioli on each slice, then top with 2 pieces bacon, 2 slices tomato, some red onion and a single piece of lettuce. Top each sandwich with another slice of bread.
Slice the club sandwiches into quarters and serve with a pickle and some potato chips.