Step 1: Combine egg, salt, pepper, sugar, mustard and vinegar in the bowl of a mixer.
Step 2: Beat at high speed until thoroughly combined, about 1 minute.
Step 3: With mixer running, slowly begin to add the oil, a few drops at a time.
Step 4: Continue beating and adding oil very slowly until all the oil has been incorporated.
Step 5: Cover and refrigerate.
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