Using a fork, smash the avocado in a medium bowl until chunky. Add a big squeeze of lime and a big pinch of salt. Continue mashing until the avocado spread reaches your desired consistency. Taste, and add more salt and/or lime as needed. Set aside.
Set a medium pot filled to 1/3rd over high heat. When bubbles begin to form on the bottom and sides of the pot, reduce heat to medium-high. Crack the eggs into separate small bowls or ramekins.
Optional: use the handle of a wooden spoon to swirl the water in one direction, like a hurricane. Add a short pour of vinegar (this often helps to keep the strands of egg together). Carefully pour one egg into the center of the whirlpool. Poach for 3 to 5 minutes, depending on how firm you like the yolk (3 for loose; 5 for slightly done). Remove the egg to a paper towel lined plate. Repeat with the other egg.
Cover the bottom of a small frying pan with a thin layer of the olive oil. Turn heat to medium. When the oil shimmers in the pan, add the bread slices. Let sit for 30 seconds, then flip (the bread will not be toasted at this point). Heat the bread until golden brown on the down side, then flip a second time. You shouldn't need more oil, but if the pan is dry at this point, add just a drizzle around the bread slices. When the second side is golden brown, remove from pan, and the let the slices cool until you can handle them.
assemble.
Spread a thick layer of the avocado on the warm fried bread slices. Top each with an egg, and sprinkle with salt and black pepper.