Place a saucepan with 1 inch of water over medium high heat. Bring to a boil. Fit with a steamer basket and reduce heat to medium. Carefully lower 6 eggs into the steamer basket. Cover and let the eggs steam for 13 minutes.
Meanwhile, put ice water in a shallow storage container with a lid. When the eggs have finished cooking, carefully remove the eggs from the saucepan and place in the storage container. Cover the container and let sit for 15 minutes.
Repeat the cooking process with the remaining 6 eggs while the first batch is sitting in the ice water.
After the first batch of eggs has chilled for 15 minutes, shake the container (with the lid still on!) until the egg shells have cracked. Remove the eggs and place the second batch of eggs in ice water in the container and repeat the chilling process for 15 minutes.
Carefully remove the shells from the first batch of eggs. I find that peeling them under running water works best. Repeat with the second batch.
When all of the eggs are peeled, slice the eggs in half lengthwise. Carefully scoop out the yolks and place in a large bowl. Use a fork to crumble the yolks.
Add the mayonnaise, yellow mustard, vinegar, and salt to the egg yolks. Use a hand mixer to beat until combined and the mixture is smooth.
Transfer the mixture to a piping bag or plastic sandwich bag fitted with a star tip (or just cut a hole in the plastic sandwich bag if you don’t have a star tip).
Pipe the egg yolk mixture into the egg whites. Place on a serving platter and serve with your desired toppings.