Place eggs in a saucepan and cover with water. Bring to a boil over medium-high heat. Once boiling, remove from heat and let stand, covered, for 9 minutes. Drain eggs and rinse with cold water for several minutes. (This can be done 1 day ahead and the hard-boiled eggs kept refrigerated.)
Peel eggs and cut in half lengthwise.
Carefully remove the egg yolks and place in a medium bowl. Set the whites aside. To the yolks, add mustard, mayonnaise, yogurt, and truffle oil. Use a fork to mash the yolks and combine all ingredients, working until it has a smooth consistency.
Using two small spoons, gently scoop the filling back into the whites. Alternatively, you can use a pastry bag fitted with a plain or star-shaped tip (or a small zip-top plastic bag with a corner cut out) to pipe mixture into egg halves. Garnish with chives, if desired — 1 chive sliver on each egg looks nice — and serve with anchovies on the side.