Slice the chorizo into small, bite-sized pieces and heat a skillet over medium heat.
Add a tablespoon of oil to the skillet and cook the chorizo until it releases its fragrant oils and turns browned and crispy around the edges, about 3-4 minutes.
Crack the eggs into a bowl and whisk until the yolks and whites are fully combined, looking smooth and slightly frothy.
Pour the beaten eggs into the skillet with the chorizo, and let them sit undisturbed for about 30 seconds until they start to set.
Gently scramble the eggs and chorizo together, stirring frequently to create a mixture with a creamy texture and some crispy bits, cooking for about 2-3 minutes until just cooked through.
While the filling cooks, warm each tortilla briefly in the microwave or on a dry skillet until soft and pliable, about 10-15 seconds.
Divide the chorizo and egg scramble evenly between the tortillas, placing it in the center of each.
If desired, sprinkle shredded cheese over the filling and add hot sauce to taste, then fold the tortillas into wraps.
Optionally, place the wraps back in the skillet for a minute per side to crisp up the tortillas and melt the cheese, if used.
Remove the wraps from the skillet, slice in half if desired, and serve immediately while hot and fragrant, with extra hot sauce on the side.