Place your eggs in a single layer in a medium saucepan and cover them with cold water by at least an inch. Bring the water to a full boil, then immediately remove the pan from the heat and cover it with a lid. Let the eggs sit in the hot water for exactly 10 minutes. Prepare an ice bath while you wait. Once the time is up, transfer the eggs to the ice bath for 5 minutes to stop the cooking process and make them easier to peel.
Gently crack the eggshells and peel them under cool running water. Pat the eggs dry with a paper towel. Using a sharp knife, slice each egg in half lengthwise. Carefully remove the yolks and place them into a medium mixing bowl. Arrange the empty egg white halves on a serving platter, cover them loosely with plastic wrap, and set them aside.
Mash the egg yolks with a fork until they are fine and crumbly. Add the mayonnaise, yellow mustard, salt, and black pepper. Mix everything together until the texture is completely smooth and creamy. If the mixture feels too dry, you can add an extra teaspoon of mayonnaise to reach the perfect piping consistency.
Split the yolk mixture evenly into two separate small bowls. In the first bowl, stir in the turmeric powder to create the vibrant gold filling. In the second bowl, fold in the basil pesto until the mixture turns a beautiful festive green. Taste both mixtures and add a tiny pinch of salt if needed to balance the flavors of the pesto and turmeric.
Transfer each colored filling into its own piping bag fitted with a star tip, or simply use a small spoon. Fill six of the egg white halves with the gold mixture and the remaining six with the green mixture. Sprinkle the gold eggs with a touch of smoked paprika and top the green eggs with freshly chopped chives. Serve immediately or chill until your Christmas guests arrive.