Preheat the oven to 450°F (232°C).
Line a small baking dish with parchment paper.
Scoop a teaspoon of flesh from the center of each avocado half to enlarge the cavity so an egg will fit.
Carefully crack one large egg into the cavity of each avocado half.
Lightly sprinkle each egg with 1/2 teaspoon sea salt and 1/2 teaspoon ground black pepper, divided among the four halves.
Place the avocado halves in the prepared baking dish so they sit stable, then bake for about 15 minutes, or until the egg whites are set.
With about 1 minute remaining, sprinkle the shredded Mexican cheese evenly over the tops and return to the oven until the cheese melts.
Remove from the oven and top each avocado cup with salsa before serving.