Heat a medium-size nonstick skillet over medium-high. Add chorizo; cook, stirring and breaking into small pieces, until meat is browned, crumbled, and cooked through, about 3 minutes. Using a slotted spoon, transfer chorizo to a paper-towel lined plate, and set aside.

Fill a large pot with water, and bring to a boil over high. Carefully lower eggs into boiling water; cook, undisturbed, for 11 minutes, 30 seconds.

Meanwhile, fill a large bowl halfway with ice, and add enough water to cover ice; set ice bath aside.

Using a spider or slotted spoon, immediately transfer cooked eggs from boiling water to ice bath. Let stand until completely cooled, at least 5 minutes or up to 30 minutes.

Working with 1 egg at a time, firmly tap eggs on countertop or a flat work surface until cracks form all over the shell. Peel eggs under cold water.

Cut eggs in half lengthwise, and carefully remove yolks. Using a fork, mash together yolks and mayonnaise in a medium bowl. Add hot sauce, salt, pepper, and 3/4 teaspoon of the lime juice. Stir well to combine.

Stir together avocado and remaining 1/2 teaspoon lime juice in a small bowl; set aside. Spoon egg yolk mixture evenly (about 1 tablespoon each) into egg whites. Top evenly with cooked chorizo, avocado mixture, and cilantro. Garnish with additional hot sauce, and serve with lime wedges. Serve immediately, or store in an airtight container in refrigerator up to 3 days.