Add eggs in a single layer to a large pan. Add salt and water until eggs are covered by at least a inch of water.
Bring water to a full rolling boil over medium high heat.
Reduce heat to simmer. Cover and pull pan slightly off burner.
Set the timer for 12-15 minutes.
Place ice and water in a large bowl.
Gently remove eggs from the hot water and add to the ice bowl with the ice water.
Let eggs completely cool.
Peel eggs by gently tapping the egg on the table all around. Start at the thicker end of the egg. Gently remove the shell and peel. The egg may have a thin, clear membrane layer. If you can remove that the shell will more easily release from the egg. Rinse to peeled egg with water.
Slice egg inhalf from the thinner end to the thicker end. Place hardened yellow in a bowl.
Rince egg half, pat dry with a paper towl and place on an deviled egg dish or plate.
Once all eggs are peeled. Take a fork and mash the yellow until crumbly.
In a separate bowl, combine yogurt, olive oil, and lemon juice. Add to yellow and mix. Next, add capers, anchovy paste, parsley, peppers, and a pinch of salt. Continue to mix and mash until the egg mixture forms a creamy thick paste.
You can at this point simply use a spoon to fill each egg half with about a tablespoon of egg filling. Another option is to take a zip lock bag and snip a tiny corner. Fill the back with egg mixture and pipe into the egg half. I like to do this but also add a pastry tip with a large opening. This gives the final egg mixture a ruffled appearance.
Sprinkle egg mixture with paprika. Garnish with chopped bell pepper, additional chopped capers, or black olives.