In a Dutch oven or other large pot, place the potatoes in a single layer. Cover with water and add a heaping teaspoon of salt. Cover and set it on medium-high heat. When the water begins to boil, set a timer for 20 minutes and lower heat to maintain a gentle boil.

Meanwhile, place the eggs in one layer in a small saucepan and cover them with water. Cover the pan and set it on medium-high heat. When the water begins to boil, set a timer for 12 to 15 minutes and reduce heat as needed to maintain the boil.

While the potatoes and eggs are cooking, mince the onion and chop the celery. Set aside, and start gathering the herbs and spices. When the timer goes off for the potatoes, start checking them for doneness with a metal skewer or sharp knife, starting with the smallest potatoes. As the potatoes become tender throughout, remove them from the pot and set them aside on a counter or cutting board to cool enough to handle (about 10 to 15 minutes).

When the timer goes off for the eggs, remove from heat and drain the water; fill the pot with cold tap water. Drain and fill the pot at least once more, until the eggs are cool enough to handle. Immediately start peeling the eggs by cracking the shell all over on the counter, then peeling them. Place the peeled eggs back in the water as you peel them to cool completely.

Peel the still-warm potatoes with a sharp knife, cutting out the stem end and any deep eyes that can’t be peeled easily. Cut the potatoes into ½ to ¾ inch pieces and add them to a large mixing bowl. Sprinkle the red wine vinegar over them, and toss to coat. Add the spices, herbs, onion, and celery and toss again to combine. Add the mayonnaise and stir gently to combine, adding more to taste. Chop the eggs into the bowl and stir gently to combine. Refrigerate for at least 2 hours to let the flavors combine.