When it comes to mayonnaise, it is somewhat a matter of taste/religion whether you use a soft or hard whisk, an immersion blender, or a mixer. It doesn't matter what you use, as long as it is whipped hard, it will succeed.

It basically takes only a few minutes to whip up a mayonnaise, but it's important to manage the temperatures. So make sure the eggs are out of the fridge well in advance (preferably one hour before) so they are at room temperature when it's time to whip.

Start by whisking the yolks with mustard, salt, and vinegar.

When they have an eggnog-like consistency, add a little oil at a time while whisking vigorously.

Gradually add more oil, and the more oil you add, the thicker it becomes.

Continue until it has the desired thickness; it should be able to stand on its own.

Season to taste with pepper and lemon juice.