Put the bacon on a sheet pan lined with foil. Bake until crispy, 18 to 20 minutes.
Meanwhile, make the cilantro mayo: Mix the mayo with the chopped cilantro and a pinch of salt and pepper in a small bowl. Set aside.
Preheat a large cast-iron skillet over medium heat.
For the patties, mix the chuck, chorizo, green chiles, a pinch of salt and 1/4 teaspoon black pepper in a large bowl until combined well. Pinch off a fourth of the meat mixture, forming it into a disc. Repeat with the remaining meat to make 3 more discs. Put 2 tablespoons olive oil in the preheated skillet, then add the patties. Using the bottom of a spatula, smash the patties until they are about 1/2-inch-thick. Fry until cooked through, 4 to 5 minutes per side, then remove to a plate.
Meanwhile, start the eggs. Heat the remaining olive oil and the butter in a nonstick skillet over medium heat. Add the eggs and cook sunny-side up, 5 to 6 minutes for a slightly runny yolk. Remove the eggs with a slotted spatula to drain or remove the eggs to a paper towel-lined plate to drain.
Spread the bottom of each bun with some of the cilantro mayo and place on plates or a serving dish. Top each with a patty and 2 pieces of bacon. Top each with lettuce, tomato and an egg; drizzle with some hot sauce. Spread the remaining cilantro mayo on the bun lids, then place them carefully on top of the burgers.
Serve alongside the Taco Tots.
Preheat the oven to 425 degrees F.
Toss the potato tots and taco seasoning on a sheet pan. Bake until crisp, about 20 minutes. Remove from the oven, sprinkle over the cheese and return to the oven to melt the cheese, 5 minutes more.