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1
Whisk the egg in a bowl with the seltzer. Put the breadcrumbs in another bowl. Dip a sliced vegetable in the egg then the breadcrumbs. Repeat with the remaining vegetables.
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2
Heat oil in a large skillet and add the vegetables so they are in one layer; work in batches if necessary and don't crowd the pan. Flip once and cook until the fritters are slightly browned on each side.
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3
Transfer to a paper towel-lined plate as they finish. Serve immediately with homemade mayonnaise (recipe below).
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4
Put the egg yolk and mustard in a bowl with a pinch of salt and pepper and a dash of vinegar. Using an electric mixer, an old fashioned whisk, or an electric whisk (my weapon of choice), beat vigorously until the contents are fully combined and slightly thickened.
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5
While whisking, add begin to add the oil in a slow stream. Stop adding oil but continue whisking, until the mixture emulsifies and looks like mayonnaise.
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6
Continue adding oil in a slow stream and whisking until the mayonnaise reaches the desired consistency (which may be less than a cup of oil). I like to use about half neutral oil and half good quality olive oil, but play with it to taste.
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7
Whisk in lemon juice to taste (I like a slightly lemony mayo) and season with salt and pepper as necessary.
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8
Store in a clean glass jar or covered with plastic wrap in the back of the fridge for up to four days.