Bring a pot of water to a rolling boil, then carefully lower the eggs into the water and boil for 10 minutes. While the eggs cook, prepare an ice bath in a bowl with ice water. Once 10 minutes are up, immediately transfer the eggs to the ice bath and let them sit for 10 minutes. This stops the cooking process and makes peeling much easier—I find the ice bath is crucial for getting those clean, intact whites without any gray-green ring around the yolks.
While the eggs chill, combine the mayonnaise, sour cream, mustard, and vinegar in a bowl. Whisk these together until smooth and well blended—this creates a creamy, tangy base that will hold all the seasoning evenly.
Remove the eggs from the ice bath and peel them carefully under cool running water, starting from the wider end where the air pocket makes it easier. Once all eggs are peeled, pat them dry with a paper towel, then slice each egg in half lengthwise. Gently remove the yolks and place them in a small bowl, setting the egg white halves aside on a serving platter.
Add the cooked egg yolks to the bowl with the mayonnaise mixture from Step 2 and mash everything together with a fork until you reach a smooth, creamy consistency with no large chunks. Stir in the minced dill, garlic powder, salt, and pepper to taste. I like to taste as I go and adjust the seasoning—the dill should be evenly distributed so each bite has consistent flavor.
Transfer the yolk filling into a piping bag or a small zip-top bag with the corner cut off for easy piping, or simply spoon the mixture into each egg white half using a small spoon or ice cream scoop. Divide the filling evenly among all the egg white halves, then garnish each deviled egg with a small sprig of fresh dill snipped into 1/2-inch pieces for a pop of color and fresh flavor.