Fill a saucepan with enough water to cover the eggs by 1 inch. Add the salt and bring to a gentle boil. Once the water is boiling, gently lower in the eggs, being careful not to break them. Reduce heat to a gentle boil and cook the eggs 14 minutes. A few minutes before the eggs are finished cooking, fill a large bowl with ice water. With a slotted spoon, carefully remove the eggs from the boiling water and submerge them immediately into the ice water. Let cool completely, about 15 minutes, then peel under cool running water.
In a medium bowl, stir together the Greek yogurt, Dijon mustard, vinegar, curry, yellow mustard, cayenne, and 1/4 teaspoon salt. Cut the eggs in half from tip to tip. With a small spoon, gently scoop out the yolks and add them to the bowl with the curry mixture (for a very smooth filling, press the egg yolks through a sieve and into the bowl). Set the egg whites aside. Mash the yolks into the filling with the back of a fork until smooth. Taste and season with additional salt and cayenne as desired.
Scoop or pipe the curry mixture into the hollow egg whites (I place the mixture in a ziptop bag, then snip off the corner to pipe). Refrigerate until ready to serve. Just before serving, sprinkle with paprika and chives.
Make ahead tips: Hardboiled eggs will keep in the refrigerator for up to 1 week. Assembled deviled eggs will keep for up to two days.
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