I'd like to make the shrimp burger recipe from Cook's Illustrated but am loathe to buy mayonnaise just for that. Can I make my own using egg and oil?
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You can definitely make your own mayonnaise with egg and oil and a little lemon juice or vinegar. There are recipes wherever you find your recipe, it takes time because you have to beat in the oil slowly but it's good. Good luck
I've found the easiest way to make homemade mayo is with a stick blender. Make sure everything is at room temp and then put all the ingredients in a narrow jar (I use the one that came with my stick blender but a pint jar works too). I wait a minute to let everything settle after I put the blender into the jar before I start blending. Then blend without lifting the stick blender. You will see mayo forming on the bottom 1/3-1/2 of the jar. At that point, I tip the stick blender to pull down more oil and then very slowly pull the stick blender to the top. I've have had a few times where this didn't work but it was always when I used too wide a jar.
I can't abide the stuff myself, but my mother used to make mayonnaise in a regular blender; it only took a few seconds. As far as I remember she put in an egg and some lemon juice, then drizzled in the oil with the blender running- it should be pretty easy to come up with a recipe.