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To make the mayo, place all ingredients in a food processor and blend on high until uniform in color.
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In a large skillet, over medium-high heat, cook the bacon until crispy, about 2 minutes per side. Placed the cooked bacon on paper towels to drain the fat. Remove some of the bacon fat from the skillet, but leave enough to grill the bread in.
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Place the bread in the skillet and grill over medium heat until one side is slightly browned and crispy, about 3 minutes. Place the bread on plates to assemble the sandwiches.
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Spread the inside of each slice with chipotle mayo. Top each bottom slice of bread with lettuce, tomato, avocado, and bacon.
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In the same skillet, fry two eggs in the leftover bacon grease on medium-high heat until the whites are opaque, but the yolks are still runny, about 1 minute per side. Place one egg on top of each sandwich. Then top with the remaining bread slices.
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Serve immediately.