In a small mixing bowl, combine mayonnaise, minced chipotle peppers, lime juice, and garlic powder. Stir thoroughly until smooth and well-blended.

Heat a skillet over medium-high heat, add sausage patties, and cook for 3-4 minutes on each side until browned.

Reduce heat to medium-low, add butter to the skillet, spread it on the cut sides of the brioche buns, and toast for about 1-2 minutes until golden brown.

In a mixing bowl, whisk together eggs, milk, and a pinch of salt and pepper. Melt butter in skillet, pour in egg mixture, and cook gently until fluffy.

Spread chipotle aioli on toasted buns, layer with sausage, scrambled eggs, and cheddar cheese. Top with the bun half and serve immediately.