Place eggs in a pot and cover with cold water by about an inch. Bring to a boil over high heat, then remove from heat and stir in baking soda—this helps the eggs cook evenly and makes them easier to peel. Let the eggs sit in the hot water for 12 minutes. While they rest, prepare an ice bath by filling a bowl with ice and cold water. After 12 minutes, transfer the eggs directly to the ice bath and let them cool completely, about 5-10 minutes. This stops the cooking process and prevents that gray-green ring from forming around the yolk.

Once the eggs are completely cool, gently peel them under cool running water—the water helps separate the shell from the membrane. Pat the eggs dry with a paper towel. Slice each egg in half lengthwise, then carefully scoop out the yolks into a medium bowl, keeping the white halves intact on a serving platter. I like to arrange the egg white halves cut-side up as I go so they're ready for filling.

To the bowl of yolks, add the mayonnaise, relish, yellow mustard, white vinegar, garlic powder, salt, and pepper. Using a fork, mash everything together until smooth and creamy—don't overmix or the filling can become dense. Taste and adjust seasonings as needed; I like to add an extra pinch of salt since it really brings out the flavor of the filling.

Transfer the yolk mixture to a piping bag fitted with a large round or fluted tip, or simply spoon it into the egg white halves for a rustic look. Pipe or spoon the filling generously into each egg white half, then lightly dust the top of each deviled egg with smoked paprika for both color and a subtle smoky depth. Refrigerate until ready to serve, and these will keep well for up to 3 days.