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1
Preheat oven to 400u00b0F. Line a rimmed baking sheet with foil and arrange bacon on top in a single layer. Bake until crisp and evenly cooked, about 16 minutes, rotating baking sheet once front to back during cooking. Place bacon on a paper towel-lined plate and set aside.
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2
In the bottom of a tall, narrow container that just fits the head of an immersion blender, combine the egg yolk, water, lime juice, and a pinch of salt. In a small saucepan over high heat, melt the butter. Swirl the saucepan constantly until the butter is no longer foaming. Pour butter into a liquid measuring cup.
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3
Place the head of the immersion blender into the bottom of the container and turn it on. With the blender running, very slowly pour in the hot butter; it should emulsify with the other ingredients. Continue pouring until all of the butter has been added. Add half of the jalapeno (or enough to achieve your desired level of heat); reserve the remaining jalapeno to garnish burgers. Keep blending until smooth and creamy. Transfer to a small lidded pot and keep in a warm place until ready to use.
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4
Arrange bacon on the bottom halves of English muffins and set aside. Preheat a large saute pan or skillet over high heat. Place 2 balls of beef in the pan at a time and smash down with two stiff metal spatulas (or any flat-bottomed, heat-safe tool, such as a small saucepan). Press firmly to flatten.
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5
Season the patties generously with salt and pepper and cook until the bottoms are well browned and the tops are beginning to cook through to a pale grayish pink, about 45 seconds. Flip the patties and place a slice of cheese on top of one. Immediately stack the second one on top. Transfer the smashed-burger stack to one of the bacon-topped muffins. Repeat until all of the burgers have been cooked. Top each with sliced avocado.
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6
In a large nonstick skillet over medium heat, melt 2 tablespoons butter. Crack eggs into the skillet and fry, undisturbed, until cooked to your liking, about 2 minutes for runny yolks. Place each egg on top of the sliced avocado. Spoon the Hollandaise on top of the eggs and season with black pepper and reserved chopped jalapeno. Close burgers and serve immediately.
