Place eggs in a single layer in a saucepan. Cover with cold water by 1 inch. Bring to a rolling boil, then remove from heat, cover, and let sit for 12 minutes.
Ice bath: Transfer eggs immediately to a bowl of ice water. Let sit for 5 minutes.
Peel the eggs: Tap each egg to crack the shell, roll to create cracks all over, and peel under cool running water.
Halve and remove yolks: Cut each egg in half lengthwise. Scoop out yolks into a bowl and arrange whites on a serving plate
Make the filling: Mash yolks with a fork until crumbly. Add Greek yogurt, mustard, salt, pepper, and 1 tablespoon everything bagel seasoning. Mix until smooth.
Fill the eggs: Spoon or pipe filling into each egg white half.
Garnish: Sprinkle remaining seasoning over filled eggs. Add paprika and chives if desired.
Chill: Refrigerate for at least 30 minutes before serving.