Score potatoes all the way around the centers like a belt (see photos in post above) then place inside a large pot of cold water. Place the pot over high heat then bring to a boil. Turn the heat down to medium then simmer until a knife or skewer can be easily inserted into the centers, 20-40 minutes depending on the size of your potatoes. Avoid overcooking the potatoes or they can become mushy and mealy. Use tongs to transfer the potatoes to a colander then set aside to cool for 15 minutes.

Meanwhile, add eggs to a small saucepan then cover the tops by 1" with cold water. Place the pan over high heat to bring to a boil. Once boiling, turn the heat off then place a lid on top and let the pan sit for 12 minutes. While the eggs are sitting, fill a bowl with ice and water. Drain the eggs then add to the ice bath to cool for 10 minutes. Peel eggs then chop and place inside an airtight container. Refrigerate until ready to use.

Add vinaigrette ingredients to a bowl or jar with a tight fitting lid then whisk or shake to combine and set aside.

When the potatoes are cool enough to handle, but still warm, use a small paring knife to peel the potatoes then chop them into pieces — they don't have to be uniform and precise. Transfer to a large mixing bowl then drizzle 3/4 of the dressing over the warm potatoes and use a spatula to fold to combine. Cover and refrigerate for at least 1 hour, and up to overnight. Place remaining dressing in the refrigerator as well.

When ready to serve, drizzle remaining dressing over the chilled potatoes then add chopped hard boiled eggs, and mayonnaise (start with 1/2 cup then add more if desired). Fold to combine then taste and add more salt and/or mayonnaise if desired. Serve or place back in the refrigerator for up to 3 more days.