Prepare sourdough buns: Mix water, starter, and bread flour. Let rest, add salt, perform folds, shape into buns, proof overnight, and bake at 450°F for 20-30 minutes.
Make duck fat mayo: Blend duck egg, melted duck fat, garlic, salt, and orange juice until emulsified.
Prepare Wagyu beef: Grind Japanese A5 Wagyu beef, form into a patty, and cook to desired doneness. Season with salt.
Sauté mushrooms in cognac and butter: Sauté mushrooms until golden, deglaze with Remy Martin cognac, and finish with organic grass-fed butter.
Assemble the cheeseburger: Spread garlic duck aioli on sourdough buns, add Wagyu beef patty with Comté cheese, top with cognac sautéed mushrooms, more aioli, and the top bun.