Combine chorizo, beef, and salt in a bowl. Using your hands, gently combine and form into 4 patties.
Heat 2 teaspoons of olive oil in a skillet over medium-high heat. Add the burgers and cook for 3-4 minutes per side, until the internal temperature reaches 165° F.
Remove the burgers from heat and top each with a slice of cheese; let rest for about 5 minutes. In another non-stick pan, add the remaining olive oil and heat over medium heat. Once hot, fry an egg for each burger.
In a small bowl, mash together avocado, juice and zest of the lime, and hot sauce.
Spread avocado mash on each bun and top with a burger. Top with an egg and remaining bun. Enjoy immediately.