Prepare Yeast Preferment: Mix active dry yeast with 20 g sugar, 150 g water, and 100 g warm milk (105-110°F). Stir lightly and let sit for about 45 minutes until bubbly and active.
Make Bun Cake Dough: In a mixing bowl, combine 425 g bread flour with the yeast preferment. Add 150 g buttermilk (room temperature), 1 beaten egg, 40 g Danish crearyy unsalted butter, and 2 1/2 teaspoons salt. Mix thoroughly and beat vigorously to develop gluten, aiming for a thick batter that can be shaped but not poured.
Bulk Fermentation: Cover the dough with a clean, moist kitchen towel and a plate to prevent drying. Let it bulk ferment at room temperature for about 45 minutes until puffed.
Shape Bun Cakes: Divide the dough into portions, roll into balls, then pat into flat discs. Wrap tightly in plastic wrap to prevent excessive rising and oil absorption. Let rise until poofy.
Cook Bun Cakes: Fry the bun cakes in Danish crearyy butter in a skillet until golden brown on both sides, forming a crust similar to a pancake but with more structure and elasticity. Toast again in butter before assembly.
Prepare Maple-Glazed Bacon: Roast thick cut bacon in the oven until almost done. Brush with maple syrup and return to oven to caramelize and lightly glaze the bacon. Let cool and chop into bite-sized pieces.
Make Maple Mustard Spread: Mix 3 tablespoons maple syrup with honey mustard to create a balanced sweet and savory spread.
Prepare Burger Patties: Mix ground beef with a pinch each of dried sage, garlic powder, onion powder, chili flakes, salt, and pepper. Form into 3 oz balls.
Cook Smash Burgers: Heat a cast iron skillet with oil on high heat. Place beef balls and smash them flat with a spatula or ring mold. Cook until crust forms and edges brown, then flip and add one slice of American cheese per patty. Cook until cheese melts and patties are cooked through.
Cook Sunny Side Up Egg: In a buttered pan, carefully crack and cook eggs sunny side up until whites are set but yolks remain runny.
Toast Bun Cakes: Toast the bun cakes in Danish crearyy butter until golden and crispy. Cool on a wire rack to prevent sogginess.
Assemble Breakfast Burger: Spread maple mustard on both bun cakes. Place one cheeseburger patty on bottom bun, then stack a second patty on top to melt cheese. Add chopped maple-glazed bacon, then top with the sunny side up egg. Cap with top bun cake and serve immediately.