Place eggs in a saucepan in a singe layer. Cover with an inch of water, place over medium-high heat and bring to a boil. Immediately turn off the heat and cover. Let the eggs sit in the water for 2 minutes, then transfer to a bowl of ice water. When cool enough to handle, peel and slice the eggs.
Toast the rye bread. Arrange on a plate and drizzle with olive oil. Arrange the sliced beets, avocado and eggs on top and season with salt.
Top toasts with chopped walnuts and flax seeds and a drizzle of your best extra virgin olive oil.