Break 1 egg and 2 tablspoons lemon juice in the food processor or blender and let it sit from 30 minutes - 2 hours. I generally let it sit about 1 1/2 hours.
After you are positive it is room temperature:

Add 1/2 teaspoon dry mustard and 1/2 teaspoon salt
Add 1/4 cup oil (I typically do use extra virgin olive oil for this step)

Blend for 1 minute.

Now it is time for the rest of the oil:

VERY SLOWLY drizzle in 1 additional cup of oil. I like hazelnut, if you use olive then make certain it is a very light olive oil or the taste will be too strong.
Did I mention to drizzle VERY SLOWLY? It takes me 3-4 minutes to drizzle in the cup of oil. If you are using a food processor the sound pitch will change as the liquid begins to form the emulsification.

The texture will be a bit creamier if you use a food processor, a bit thicker if you use a blender. I use the food processor because it is less messy As long as I've made VERY certain the egg and lemon juice are at room temperature and been patient enough when drizzling the cup of oil this recipe has never failed me. This doesn't make a large amount, and it will last until the expiration date on your egg carton.