1 loaf good-quality brioche or challah, cut into 12 slices (you might have bread left over)
Olive oil, as needed
1 egg yolk
1 1/2 teaspoons Dijon mustard
1 teaspoon cider vinegar
Salt
8ounces hearts of romaine, leaves separated, rinsed, and dried
1pound ripe tomatoes (preferably an heirloom variety), thickly sliced
Instructions
Heat the oven to 400°F and position one of the racks as high as it can go, with another rack in the middle of the oven. Line a large rimmed baking sheet with foil to help with cleanup and put a wire rack on top. Put half the bacon slices into a medium bowl; sprinkle with lots of pepper, toss, and spread out on the rack in a single layer. Repeat with the remaining bacon slices, sprinkling with just the sugar, and putting them on the rack as well.
Transfer the pan to the oven and roast, undisturbed, until the bacon is crisp and browned, 10 to 25 minutes, depending on the thickness. Put the bread slices on a baking sheet and toast in the oven on the middle rack, until both sides are as golden as you like.
When the bacon is ready, carefully lift the rack from the pan and transfer it to sit over paper towels to drain. Pour the rendered fat from the baking sheet into a heatproof measuring cup; you should have 1/2 cup; if not, add some olive oil until you do. Put the bacon on a platter, return it to the oven to stay warm, and turn it off.
Put the yolk and mustard in a medium bowl and beat with a wire whisk. Begin to add the bacon fat in dribbles as you beat, only adding more when the previous addition is incorporated. When a thick emulsion forms, then you can add the remaining fat a little faster. The whole process will take about 5 minutes. Whisk in the vinegar, sprinkle with salt and pepper, then taste and adjust the seasoning. (Use right away or refrigerate for up to 3 days.)
Spread one side of each slice of bread with mayonnaise. To assemble the sandwiches, start with one piece of bread, mayo side up, and layer with a little lettuce, tomatoes, and both kinds of bacon. Follow with another piece of toast mayonnaise side down, then spread a thin layer on the other side to help hold the sandwich together. Top with more lettuce, tomato, bacon, and the last slice of bread. Use a long toothpick or skewer to secure the sandwiches. Serve right away, passing any remaining mayo at the table.