Make your hard-boiled eggs: Place raw eggs in their shells in a large pot and cover them with enough cold water to cover the eggs by two inches.
Place the pot on your stove over medium-high heat and bring it to a boil, uncovered.
When the water is boiling rapidly, turn off the heat, cover the pot, and let the eggs sit in the water for 15 minutes.
Remove the eggs with a slotted spoon and place them in a bowl of ice water to cool.
While your eggs are cooking, rinse your potatoes in cool water and peel them, if desired. If keeping the skins on, scrub them clean, if needed.
Cut your potatoes into 1 1/4-inch chunks: Cut the potatoes in half, then in half again, and in half again until you have chunks. Place your potatoes in a bowl of water to prevent them from turning reddish brown.
When your eggs are done and removed from your pot, you can drain the water and use the same pot to cook your potatoes.
Transfer your potatoes and water to the pot and add enough extra cold water to cover the potatoes by two inches. Add a teaspoon of salt to the pot and place it on the stove over high heat, covered.
When the pot is boiling (keep an eye on it as soon as you hear it bubbling, so it doesn't spill over), lower the heat to keep the pot simmering and boil the potatoes for 10 minutes, covered, or until you can stick a fork in them with just a little resistance. (You don't want the potatoes so soft that they fall apart.)
Drain the potatoes well in a colander in the sink. Transfer the potatoes to a sheet pan in a single layer to cool off.
Peel and chop your red onion, pat the pieces dry, and add them to a large serving bowl. Rinse and pat dry your green onion. Snip off the stringy bottom tip and discard it. Use kitchen scissors (or a knife) to cut the green onion into small pieces and add them to your bowl.
Peel your cooled hard-boiled eggs, rinse them and pat them dry. Chop them into small chunks and add them to your bowl.
Pat your potatoes dry and add them to the large bowl.
In a small mixing bowl, add all of your dressing ingredients and whisk well to combine. There should be no liquid pooling on the edges.
Add your dressing to the large bowl with the potatoes, eggs and onions. Gently stir with a silicone spatula to combine. Cover with plastic wrap and chill in the refrigerator for at least six hours, but preferably overnight.
Serve chilled. Do not leave the potato salad out of the fridge for more than two hours. Place it over a tray of ice if needed for a party.
Store leftover potato salad covered in the refrigerator for up to four days after making it.
This recipe calls for 4 hard-boiled eggs, but consider boiling extra eggs at the same time so you can use them for breakfast and salads.