Place the eggs in a single layer at the bottom of a medium saucepan and cover with cold water by at least one inch.
Bring the water to a full rolling boil over high heat.
Immediately remove the pan from the heat, cover with a tight-fitting lid, and let the eggs sit for exactly 12 minutes.
While the eggs are sitting, prepare a large bowl filled with ice and cold water.
Use a slotted spoon to transfer the eggs to the ice bath and let them cool for at least 5 minutes to ensure easy peeling.
In a small mixing bowl, whisk together the Greek yogurt, Dijon mustard, and chopped chives until the dip is smooth and creamy.
Gently crack and peel the eggs under cool running water.
Slice the eggs in half and season them with sea salt, black pepper, and a dusting of smoked paprika.
Serve the seasoned eggs immediately with the yogurt dip on the side.