Cook egg in a small saucepan of gently boiling water 4 minutes. Immediately transfer to a bowl of ice water and stir until egg is cool to the touch, about 1 minute. Carefully peel egg (the yolk will still be runny). Puree in a blender with oil, almonds, lemon juice, and garlic until mixture is very smooth. Add 2 large ice cubes and puree, scraping down sides as needed, until a thick, foamy, white, emulsified sauce forms, about 1 minute. Season with salt and pepper. Blend in another ice cube if needed to thin sauce (aioli will firm slightly if chilled). Aioli can be made 3 days ahead. Cover and chill.