In a small mixing bowl, combine ½ cup of mayonnaise, 1-2 minced chipotle peppers in adobo sauce, 1 tablespoon of freshly squeezed lime juice, and 1 clove of minced garlic. Stir until creamy and smooth.

Set the aioli aside while preparing the sandwich.

Heat a skillet over medium heat, add 1 tablespoon of butter, and toast the brioche buns cut-side down until golden brown.

In the same skillet, add more butter if necessary and crack in 2-4 large eggs. Cook until whites are set but yolks remain runny, adding slices of pepper jack cheese in the last minute.

Spread chipotle aioli on toasted bun sides, layer with arugula, cheesy eggs, and slices of avocado. Top with other bun half.

Cut sandwiches in half for easy handling and serve warm.