Add the egg, crushed garlic, and about a quarter cup of olive oil to a tall blending beaker.
Place the hand blender right at the bottom, switch it on, and blend until everything starts to come together.
Keep blending while slowly pouring in the remaining oil, gently moving the blender as the mixture thickens.
Once the aioli reaches a thick, creamy consistency, blend in lemon juice and a pinch of salt.
Taste and adjust with more lemon juice or salt if needed.
Chill before serving for the best flavor and texture.