1: Place the slices of bacon in a single layer in a cold heavy large skillet and heat over medium heat. Cook the bacon until it is crisp and browned and most of the fat has melted out (rendered), about 6 minutes, turning the bacon over with tongs once the first side is browned (about 3 minutes). Transfer the bacon to a plate lined with paper towels to drain.

2: Toast the slices of bread in a toaster until golden. Place the slices of toast on a clean dish towel (this prevents the steam from making them soggy). Spread each with some of the mayonnaise. Top 2 of the slices with arugula, then with slices of tomato, bacon, and avocado. Place the remaining 2 slices of bread on top, mayonnaise side down, and cut the sandwiches in half on the diagonal before serving.