Cook the hashbrown: Heat a thin layer of oil in a skillet over medium heat. Cook the hashbrown patty until deeply golden and crispy on both sides. Transfer to a paper towel-lined plate and lightly salt.
Cook the chorizo: In the same pan, add the chorizo patty. Cook over medium heat, pressing slightly, until browned and cooked through, about 3–4 minutes per side. Set aside.
Make the avocado mash: In a small bowl, mash the avocado with lemon juice, sea salt, black pepper, and a pinch of red pepper flakes. Set aside.
Cook the eggs: Wipe out the pan and melt butter over medium-low heat. Whisk the eggs, then pour into the pan, letting them spread into a thin, even layer.
Once the eggs are just set, place the cheese in the center. Fold the sides inward (like a square or rectangle) so the eggs wrap around the cheese and fit the shape of your sandwich. Let it melt for another 30–60 seconds.
Toast the Roll: Lightly toast the sesame roll until warm and slightly crisp.
Build the Sandwich: Spread the mashed avocado on the bottom half of the roll. Layer on the crispy hashbrown, chorizo patty, and cheesy folded eggs. Close the sandwich and serve immediately.