Place eggs in a medium saucepan; add cold water to cover by 1 inch. Bring to a rolling boil. Remove pan from heat; cover, and let stand 13 minutes. Drain, and run eggs under cold water to cool them.
Meanwhile, in a medium bowl, mix together mayonnaise, mustard, vinegar, shallot, and hot sauce.
Peel eggs, and halve lengthwise; remove yolks, leaving whites intact. Transfer yolks to bowl with mayonnaise mixture, and season with salt and pepper. Mash with a fork until smooth.
Mound yolk mixture into whites. Sprinkle with paprika just before serving, or cover with plastic wrap and refrigerate up to 8 hours.