In a small bowl, mix mayonnaise, maple syrup, and Sriracha until smooth to create the maple aioli. Set aside.

Butter the brioche buns and toast them on a hot griddle or skillet until golden brown. Remove and set aside.

Divide the sausage into four portions, roll into balls, then smash thin on the hot griddle. Cook until crispy and browned on both sides.

Crack eggs onto the griddle and gently swirl the yolk once with a spatula for a marbled effect. Cook until the whites are set.

Place the sausage patties and cheese slices onto the eggs. Add a splash of water to the griddle and cover with a melting dome to steam the cheese until melted.

Spread maple aioli onto the toasted buns. Add the egg, sausage, and cheese stack, then close the sandwich.

Let the sandwiches rest for 1 minute before serving to allow the layers to set.