In your tall container, add the 2 egg yolks, salt, white pepper, and Dijon mustard.

Add the two ice cubes along with a tiny splash of water.

Pour a very small amount of oil into the container (just enough to cover the yolks).

Place the immersion blender at the very bottom of the container.

Turn it on high and hold it still at the bottom for about 5–10 seconds until you see the bottom layer turn white and creamy.

While the blender is running, begin pouring the remaining oil in a very slow, thin stream (like a thread).

Technique: Keep the blender at the bottom until the mixture thickens significantly.

Only then, slowly tilt and lift the blender head upward to pull the remaining oil into the emulsion.

Do not lift it out completely, or the mixture may break.

When you have incorporated about half of the oil, add the white vinegar (or lemon juice).

This will lighten the color of the mayonnaise and help stabilize the emulsion.

Continue adding the rest of the oil. If the mayonnaise becomes too thick or starts to look "oily/greasy," add a few drops of ice-cold water.

This will "relax" the mixture and keep it smooth.

Once all the oil is incorporated, continue to move the blender up and down a few times until the texture is perfectly smooth and stiff.

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Transfer the mayonnaise to a clean glass jar.

Place it in the refrigerator for at least 30 minutes before serving; this allows the flavors to meld and the consistency to firm up even more.