If using regular yogurt, line a strainer with a coffee filter, place over a bowl or cup, and place yogurt in the filter. Let drain for 4 hours or overnight. Discard the water and use the remaining yogurt in the recipe.
Place eggs in a pot and cover with cold water so that it covers the eggs by 1 inch. Heat on stove until boiling. Remove from heat and cover with lid. Set timer to 15 minutes.
After 15 minutes, immediately drain eggs and run under cold water or immerse in a ice bath. Peel eggs.
Slice eggs in half and scoop out yolks into a small bowl. Set the whites aside.
Smash the yolks with the back of a fork. Add 1/2 cup yogurt and mix well. Continue to add 1 tbsp of yogurt until desired consistency is reached.
Mix in sun-dried tomatoes, salt, and paprika.
Heat oil in a skillet over medium-heat. When oil is hot, test with a shallot; when the shallot instantly sizzles it is ready. Cook shallots in oil until browned. Drain on paper towels and salt lightly while still hot.
Using a small spoon, fill each egg half with the yolk mixture. Top each egg with one or two shallot slices immediately before serving.