In a bowl, whisk together 2 1/2 tsp (10g) instant yeast and 3/4 cup (185ml) whole milk at 90°F (32°C) until dissolved.
In the bowl of a stand mixer, mix together 3 cups plus 2 tbsp (469g) all-purpose flour, 3 1/2 tbsp (50g) granulated sugar, and 1 1/2 tsp (5g) fine sea salt.
Add 1 egg yolk and 2 whole eggs to the milk mixture and whisk together until homogeneous.
Add the liquid to the dry ingredients and mix with a dough hook or spiral attachment until a rough dough forms.
Add 3 tbsp (42g) unsalted, softened butter and mix for another 2-3 minutes until the dough is smooth and extensible.
Roll the dough into a rough ball and place in a greased bowl. Cover with plastic wrap and let rise for 1 1/2 hours at room temperature or until doubled.
Divide the dough into 10 even pieces weighing 80-90g each. Roll each piece into a ball and place on a baking sheet lined with parchment paper. Lightly tent with greased plastic wrap and let proof at room temperature for 30-45 minutes or until nearly doubled.
Brush the buns with egg wash consisting of 1 egg whisked together with a splash of water until smooth. Sprinkle with raw, untoasted sesame seeds.
Bake in the preheated oven for 15-17 minutes or until golden brown.
In a large pan, heat enough vegetable oil to coat the bottom over medium-high heat. Add 1 diced white onion and cook for 4-5 minutes or until softened and lightly browned. Remove from pan and set aside.
In the same pan, add enough vegetable oil to coat the bottom again. Once hot, add 1/2 lb (227g) sliced shiitake mushrooms and cook until golden brown. Season with salt and set aside.
Cook 1 lb (454g) bacon in the oven or in a pan until crispy. Drain on a paper towel.
Divide 2 lbs (900g) ground beef into 4-5 oz balls. Heat a medium-sized skillet over medium-high heat with just enough oil to create a slick. Once hot, add 1 ball of beef and press down with a spatula or press until it's about 1 inch wider than the buns and around 1/2 inch thick. Season generously with salt and pepper. Let sear for 1-2 minutes, then flip and season the other side with salt and pepper. Add a slice of American cheese and let sear for another minute. Remove from pan and repeat with the remaining beef balls.
To assemble the burgers, spread a generous amount of mayonnaise on the bottom and top buns. Drizzle with yellow mustard and ketchup. On the bottom bun, add a shingling of dill pickles, 2-3 slices of cooked bacon, a double patty with a slice of cheese on each, a slice of beefsteak tomato, seared mushrooms, griddled onion, and rough chopped iceberg lettuce. Top with the top bun.
Serve and enjoy!
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