Bring a pot of water to rolling boil. Lower room temperature eggs into boiling water and cook for exactly 6 minutes 30 seconds.

Transfer cooked eggs immediately to ice water bath to stop cooking. Let sit 2-3 minutes before peeling.

In food processor, pulse garlic and pine nuts until chopped. Add basil and pulse until coarsely chopped.

With processor running, slowly drizzle in olive oil until desired consistency. Add Parmesan and pulse to combine. Season with salt and pepper.

Toast bread slices until golden brown and crispy outside but tender inside.

Mash avocados with lemon juice and salt, leaving some texture for visual interest.

Spread generous layer of pesto on each toast. Top with mashed avocado, spreading evenly.

Slice peeled eggs in half lengthwise. Place two halves on each toast, cut-side up. Sprinkle with sea salt, pepper, and serve immediately.