Place six whole eggs in a single layer in a saucepan. Cover with enough water that there are 1 1/2 inches of water above the eggs. Cook saucepan over high heat until water begins to boil, then cover, turn the heat to low, and cook for 1 minute. 

Remove saucepan from heat and leave covered for approximately 14 minutes. Then rinse saucepan under cold water continuously for 1 minute.

Crack egg shells and carefully peel under cool running water. Gently dry with paper towels. Slice the eggs in half lengthwise. Removing the yolks with a spoon and put into a medium-sized bowl. Place the whites on a serving platter. Sprinkle whites with sea salt, fresh ground black pepper, and smoked Spanish paprika. 

Use a fork to mash the yolks into a fine crumble. Add Creme Fraîche, vinegar, mustard, salt, pepper, and cayenne. Mix ingredients well. Evenly disperse heaping teaspoons of the yolk mixture into the egg whites. Sprinkle yolks with paprika and serve.