Place eggs in a saucepan, cover with cold water, and bring to a boil over high heat. Reduce heat, and simmer for exactly 9 minutes. Pour off most of the water and immediately run cold water over eggs.
Crack eggshells and peel eggs under running water. Cut a small sliver off both ends of each egg and halve them crosswise, forming round cups. Remove yolks, and reserve. Pass yolks through a fine sieve into a bowl (or mash 'em with a fork like I did.) Add mayonnaise, vinegar, mustards, cayenne, and curry powder to bowl, and mix together with a rubber spatula until smooth. Season to taste with salt and pepper.
Spoon egg-yolk paste into a pastry bag with a star tip and pipe mixture into egg whites to form rosettes. (Or use a teaspoon to mound yolk into egg whites.) Sprinkle top of eggs with paprika.