Using a medium bowl, whisk together egg yolks, mustard, and lemon juice until smooth. Add the oil, a drop at a time, whisking until the mixture starts to thicken. Season with salt and pepper. Transfer to an airtight container and refrigerate until needed.
Heat oven to 450°F Using a rolling pin, flatten each slice of bread to 1/8-inch thickness. Using a 2-inch cookie cutter, cut 4 rounds from each slice of bread. Press rounds into mini-muffin pans forming shallow cups and bake until light brown, about 6 minutes. Cool slightly, transfer to a wire rack and cool completely. Store in an airtight container.
Remove center rib of lettuce leaves and cut leaves into 1/8-inch strips.
Using a large saute pan over medium heat, cook bacon until crisp. Drain on paper towels, crumble and set aside.
Using a large bowl, toss together bacon, lettuce and tomato. Add 2 tablespoons mayonnaise, adding more if needed just to bind mixture. Season with salt and pepper.
Fill toasted cups with a heaping teaspoon of the bacon mixture, sprinkle with chives and serve immediately. Store remaining mayonnaise in an airtight container, refrigerated up to 2 days.