This method works best with an immersion blender and a narrow container that’s just slightly wider than the blender head. The beaker that comes with most immersion blenders is perfect and helps the emulsion form quickly.
Crack 1 egg into the bottom of the container. I’ve tested this many times, and a room-temperature egg gives the most consistent, reliable results with this method. If needed, place the egg in a bowl of warm tap water for 5–10 minutes.
Add 2 tablespoons white wine vinegar, 1 tablespoon lemon juice, 1 teaspoon mustard powder, 1 teaspoon salt, and 1/4 teaspoon garlic powder directly into the container with the egg.
Pour in 1-1/4 cups oil, letting it settle on top of the egg and other ingredients. I usually let it sit for about 30–60 seconds so everything naturally separates before blending.
Place the immersion blender all the way at the bottom of the container, directly over the egg. Turn the blender on high and hold it steady without moving. Within 15–20 seconds, the mixture at the bottom will turn thick and white.
Once the emulsion forms, slowly lift the immersion blender upward to incorporate the rest of the oil. As soon as everything is blended and creamy, stop blending to avoid breaking the mayo.
Transfer the mayo to an airtight container and refrigerate. It will thicken slightly as it chills and keep well for up to 1–2 weeks.