Prepare Eggs for Boiling: Fill a medium saucepan with enough water to cover the eggs by about an inch. Bring the water to a vigorous boil over a medium-high heat setting.
Cook Eggs: Using a slotted spoon, gently lower the 3 eggs into the boiling water one by one. Reduce the heat slightly to maintain a steady, rolling simmer. Cook for 7-9 minutes for a perfectly soft-boiled, jammy yolk.
Toast Bread: While the eggs are simmering, place the 3 bread slices in a toaster or under a broiler until golden brown and toasted to your preference.
Prepare Avocado Spread: In a small bowl, combine the flesh of $frac{3}{4}$ avocado with the $frac{1}{2}$ teaspoon of fresh lemon juice. Mash with a fork until it reaches a spreadable consistency, either mostly smooth or with some small chunks.
Cool and Peel Eggs: Once the cooking time for the eggs is complete, immediately transfer them from the saucepan to a bowl filled with ice water. Allow them to chill for at least 2-3 minutes. This halts the cooking process and makes them easier to peel.
Assemble Toasts: Gently peel the cooled eggs. Slice each egg lengthwise into quarters.
Dress the Toast: Spread the prepared avocado mixture evenly over each of the 3 toasted bread slices (using approximately $frac{1}{4}$ of a whole medium avocado's worth of flesh per slice).
Final Touches: Arrange one sliced egg (four quarters) on top of the avocado layer on each toast. Season lightly with salt and a pinch of red pepper flakes, if using. Finish by drizzling 1 teaspoon of pesto over each assembled toast.
Serve: Enjoy immediately for the best experience.