In a small bowl, combine mayonnaise, minced chipotle peppers, adobo sauce, freshly squeezed lime juice, and garlic powder. Whisk together until smooth to create a creamy chipotle aioli.

Preheat a skillet over medium-high heat and add sausage patties. Cook for 3-4 minutes on each side until golden brown and cooked through.

Reduce the skillet temperature to medium and add butter. Split the brioche buns and toast them cut side down in the skillet for 2-3 minutes until golden brown.

In a mixing bowl, whisk together eggs, milk, salt, and pepper. In the skillet, add more butter and pour in the egg mixture. Stir gently until soft and fluffy, about 4-5 minutes.

Spread chipotle aioli on both halves of the toasted buns. Layer a sausage patty, half of the scrambled eggs, and a slice of cheddar cheese on the bottom half. Top with the other half of the bun.