Preheat the oven to 425° F. Slice the avocado in half, compost the pit. Scoop out a bit of the avocado to make a larger and deeper cavity (to hold the eggs).
Crack an egg over a measuring cup with a spout or something similar. Cradle the egg yolk gently in one-half of the egg shell, while letting the egg whites drain down into the measuring cup. The goal is to separate the egg whites from the yolk, it may be necessary to gently disconnect some of the egg whites from the yolk with your fingers. Gently tip the yolk, being careful not to break it, into a shot glass or other very small cup. Repeat the process of separating the yolk from the whites with a second egg, combining the whites but keeping the two yolks apart.
Gently whisk the egg whites, to break them up, then carefully divide them between the two avocado halves. Depending on the side of your eggs and avocados, you may have too much egg whites for your avocado halves. If the avocados are almost filled and you have excess egg whites, set them aside for another use (do not over-fill the avocados).
Place the avocado halves on a baking sheet, making sure they're level. It may be necessary to insert some folded parchment paper or other oven-safe material under the tips of the avocado halves to level them. Bake in the preheated oven for approximately 20 minutes until the whites are firm.
Remove the avocado halves from the oven and gently tip one yolk onto each of them (use a spoon to steady the yolk on the surface of the avocado and position it, if necessary). Return the avocado halves to the oven for an additional 5 minutes, maximum, to cook the yolks slightly while still keeping them runny.
Transfer the avocado to a plate, and top with salsa, queso fresco, cilantro, red chili flakes, jalapeno, and salt and pepper. Serve warm.