Make the guacamole: cut the avocado carefully in half, slicing gently around the seed. Remove the seed. Scoop one half of the avocado onto a cutting board. Add the remaining salt and pepper and the lime juice. Mash and mix with a fork.
Take the remaining 1/2 avocado peel-side-down in the palm of your non-dominant hand; using a paring knife, carefully make ~1/4" slices along the length of the avocado (be VERY careful not to go through the peel! See Recipe Note 2). Gently scoop the slices out of the peel with a spoon and arrange on plates.
Crack eggs into separate ramekins. Heat 2 tbsp. of the oil in a non-stick skillet over medium heat. When the oil is hot, gently add the eggs and sprinkle each with 1/4 tsp. of the salt and 1/8 tsp. of the pepper. When the egg whites are starting to set up and turn white, add a cover (preferably see-through) and reduce heat to low. Remove the egg from the heat when the egg white is fully cooked, but before the yolk turns pale.
Meanwhile, place a cast-iron skillet over medium-high heat. Brush the tortillas evenly with olive oil on both sides and lay in the skillet. When the tortillas are toasted on one side, flip them and toast the other side. When both sides are nicely toasted, remove the tortillas to a plate.
Add some guacamole schmeer to each tortilla and set on a plate. Top each with an egg and a drizzle of salsa verde. Garnish with cilantro, onions, and avocado slices and serve.