Place the 12 large eggs in a single layer at the bottom of a large saucepan. Cover the eggs with cold water so the water sits about 1 inch above the eggs.
Set the pan over high heat and bring the water to a full rolling boil. As soon as the water is boiling hard, turn off the heat and remove the pan from the burner.
Cover the pan with the lid and let the eggs sit in the hot water for 12 minutes. Set a timer so the yolks stay bright yellow and creamy instead of turning dry or gray-green.
While the eggs sit, fill a large bowl halfway with cold water and a generous amount of ice.
When the 12 minutes are up, use the spider strainer or a slotted spoon to move the eggs into the ice bath. Let the eggs chill for at least 10 minutes, until they feel completely cool to the touch.
Gently tap each egg on the counter to crack the shell all over. Roll the egg lightly under your palm to loosen the shell.
Start peeling from the wider end, where there is a small air pocket. Peel under a thin stream of cool running water if any bits of shell stick.
Pat the peeled eggs dry with paper towels so the filling can be piped neatly later.
Set the peeled eggs on a cutting board and slice each one in half lengthwise with a sharp paring knife. Wipe the knife with a damp paper towel every few cuts to keep the whites clean.
Gently pop each yolk out with a small spoon and place all the yolks in a medium mixing bowl. Arrange the 24 egg white halves cut side up on your deviled egg platter or a rimmed plate.
Mash the yolks with a fork until no large chunks remain, or use a hand mixer on low speed.
Add the 1/2 cup mayonnaise, 2 teaspoons Dijon mustard, and 1 teaspoon white vinegar.
Add the 1/2 teaspoon hot sauce if you are using it, along with the 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Stir in 1/2 teaspoon of the paprika, saving the remaining 1 1/2 teaspoons for the tops. Mix until the filling is smooth, creamy, and light, then taste and add a pinch more salt if needed.
If the filling seems too thick to pipe, add a small splash of mayonnaise, 1 teaspoon at a time.
Fit a piping bag with a large star tip, then fold the top of the bag over your hand to make it easy to fill. Spoon the yolk filling into the bag and twist the top closed.
Pipe the filling into each egg white half, making a generous rounded mound that sits slightly above the edge. If you do not have a piping bag, use a zip-top bag with one corner snipped off, or simply spoon the filling in.
Dip the tip of a toothpick in a little water so it glides without dragging the filling.
Press the toothpick into the top of the filling and pull it down the side in a gentle curved line. Repeat around the mound, making 4 to 6 lines, so each egg looks like a tiny ridged pumpkin. Wipe the toothpick clean whenever it picks up filling.
Sprinkle the remaining 1 1/2 teaspoons paprika over the eggs, using a fine-mesh strainer if you have one for an even coating. Cover the filling as fully as you can so each pumpkin gets a rich orange color.
Cut the chives into pieces about 1 inch long, so you have 24 stems. Press one chive piece into the top center of each pumpkin so it stands upright like a stem.
Cover the platter loosely with plastic wrap and refrigerate for at least 30 minutes. Chilling firms up the filling so the pumpkin ridges hold their shape.
Serve cold, straight from the refrigerator, and keep the platter out for no more than 2 hours at a party.