Whisk together the egg yolk, salt, mustard, and vinegar in a roomy bowl. To add the oil, start whisking the yolk mixture and let the oil fall from the spout, drop by drop, until you have achieved a thick, velvety mayonnaise. Taste it. Add lemon juice, salt, and pepper until the balance is to your liking.
Heat the olive oil in a saute pan. Fry the shrimp until just cooked through and still juicy. Arrange the shrimp on a platter with the mayonnaise in a dish alongside, for dipping.