To make the hard-boiled eggs, place your eggs in the bottom of a pot and cover them with cold water so that the water is at least an inch above the eggs. (Consider making extra eggs to have on hand for the next few days.) Heat, uncovered, over medium-high heat, until it comes to a rolling boil. Turn off the heat, cover the pot, and let the eggs sit for 15 minutes.
Using a slotted spoon or fine-mesh strainer, remove the eggs and place them in a bowl of ice water. When they are cool enough to touch, peel them by tapping the bottom of each egg on the counter, peeling off some shell at the bottom, and sliding the back of a teaspoon underneath the shell/skin to remove the rest of the peel. Discard the shells and rinse the eggs to remove any shell pieces. Pat the eggs dry with a paper towel. Cut the eggs into fourths and set them aside.
While your eggs are cooking, make the dressing. Place all of the dressing ingredients in a jar or plastic container with a lid and shake to mix. (Or, whisk everything in a small bowl.)
Place all of your desired toppings into small bowls. To serve, place some lettuce in a plate or bowl, add your toppings, and spoon on the dressing. Serve with a lime wedge and squeeze on some lime juice.
Store dressing and any leftover toppings covered in the refrigerator. (I like to place all of my bowls on a tray and refrigerate the tray.) Leftover, cooked eggs without their shells should be eaten within three days. (If you made extra eggs, keep them with shells on for up to a week, covered in the refrigerator.)