Bring a large pan of water to a rolling boil and then reduce heat to medium, so that the water is boiling but not overly so. Gently drop the eggs into the water, taking care not to break the shells. Allow to boil for 5 minutes, then turn off the heat, cover the pot, and let the eggs sit in the hot water for another 5-10 minutes. Remove the eggs from the water.
Under cold running water, peel away the shells and set each egg aside. Discard the shells. Slice each egg in half and scoop out the yolks into a medium sized bowl. Add the mustard, olive, mayonnaise, apple cider vinegar, and lemon. Mix together until well blended and there are no more lumps. Season to taste with salt and pepper.
Spoon the mixture back into the hollow of each egg. Sprinkle with paprika, if you wish. Serve cold.