Preheat your oven to 450°F. Line a baking dish with foil for easy cleanup. Look for a small baking dish that would allow the avocado halves to stand upright.
Cut the avocado in half lengthwise and remove the pit. Using a spoon, scoop out a little of the flesh of each avocado half - you want it to be large enough to accommodate a medium egg.
Season the avocado halves with half of the kosher salt and black pepper, and place them in the prepared baking dish.
Break each egg into a small bowl, then carefully slide the yolk, and as much as will fit from the white, into the center of each avocado half.
Bake until the whites are set, for about 15 minutes. If the egg yolks have developed a thin crust, you can carefully remove it with a small, sharp knife.
Season the avocado egg with the remaining kosher salt, freshly ground black pepper, and red pepper flakes. Garnish the dish with chopped parsley. Serve immediately.
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Notes
It's best to use a large, not-too-ripe avocado at room temperature when making this recipe. When you scoop out some of the avocado's flesh to make room for the egg, make a wide, shallow cavity, not a deep one, to ensure even cooking of the egg white.
If your eggs are large, it's best to separate the yolks from the whites, slide the yolk into the cavity first, and then pour just enough of the whites to fill the cavity, discarding the rest.
Sometimes, the yolk develops a thin crust after 15 minutes in the oven. You can leave it intact or carefully remove it using a small sharp knife. Both options look great, so this is purely up to you.
If you end up with leftovers, you can store them in the fridge, in an airtight container, for up to two days. Reheat them covered in the microwave. But it's best to only make as many as you plan on eating immediately. The leftovers don't keep too well.