Place eggs in a saucepan and cover with cold water. Bring to a boil. Turn off heat, cover and let sit in the hot water for 15 minutes. Run under cold water and peel under running water.
Slice the hard-boiled eggs in half lengthwise and gently remove the yolks. Transfer the yolks to a prep bowl. Stir in the mayonnaise (or yogurt), vinegar, dill, garlic powder and paprika. Gently fold in the diced cucumber; season with salt and pepper.
Arrange the egg halves on a platter and fill the cavities with the yolk mixture. Top each with a cucumber slice and a light sprinkle of coarse salt; cover and refrigerate until ready to serve.