This I have made many times over the last 8 years in my goal to get away from additives and preservatives. The only thing with this is since it does not have the preservatives in it I have only kept it in the fridge for no more than 2 to 2 1/2 weeks, this recipe can be doubled easy, I have never halved the recipe, if you do I guess you could use a very small egg.
1/2 tsp dry mustard
2 tsp distilled white vinegar
1/4 cup vegetable oil
1/2 tsp salt
3/4 cup olive oil
Add all ingredients in a blender except the 3/4 cup Olive oil, blend 2 to 3 minutes, then very slowly in a thin stream add the 3/4 cup olive oil this will take a few minutes so don't get in a hurry. After all the olive oil has been added continue blending for a few more minutes until the mixture gets thick. Transfer to the fridge. (I put the mixture in a clean glass jar).
Remember this does have raw eggs in it, I am not to concerned with the eggs I use, they are from our free range hens here on the farm. I don't know what you should do if your eggs are from the store, sorry, but I am sure you can check into this on the Internet. Again this has no preservatives in it so I would not keep in the fridge longer than 2 to 2 1/2 weeks.
I have also on occasion added 1/2 cup of my homemade zucchini relish before putting into the fridge. I have also omitted the dry mustard and replaced it with 1/4 cup of lemon juice ( juice of about one lemon).