Cube your potatoes. Wash your red potatoes well — we're leaving the skins on. Cut them into ½ to 1-inch pieces, trying to keep them fairly uniform so they cook evenly. About 3 to 4 small red potatoes will give you a pound. Yellow potatoes work fine here too if that's what you have.
Add potatoes and eggs to a pot. Place your cubed potatoes in a medium pot. Nestle the two eggs (washed well) right down in there with them. Cover with cold water and bring to a boil over medium-high heat, then reduce the heat slightly to keep it at a steady boil.
Prep the cauliflower while the potatoes start cooking. Cut your cauliflower into small florets, similar in size to your potato pieces. After the potatoes have been cooking for about 5 minutes, add the cauliflower directly to the pot. It cooks faster than the potatoes, so adding it midway through keeps everything finishing at the same time. Let it all go for another 5 to 7 minutes until both the potatoes and cauliflower are fork-tender.
Prep the celery and onion. While the vegetables are cooking, finely dice your celery and onion. You want small pieces here — they're adding flavor and a little crunch without overwhelming any one bite.
Drain and cool. Remove the eggs and set them aside. Drain the potatoes and cauliflower and spread them out on a sheet pan — this helps them cool down faster. Immediately sprinkle with ¼ to ½ teaspoon of salt while they're still hot. The warmth helps that seasoning soak right in.
Ice bath the eggs. Peel your eggs once they've cooled enough to handle, or pop them in an ice water bath for a few minutes to stop the cooking and make them easier to peel.
Make the dressing. In a medium bowl, whisk together the sour cream, mayonnaise, mustard, dill relish, parsley, pickle juice, and salt. Taste and adjust as needed. Everything in this dressing should have that dill flavor — don't reach for sweet relish by mistake.
Combine. Once your potatoes and cauliflower are no longer piping hot (still slightly warm is fine), add them to a large bowl. Add the diced celery and onion. Chop your eggs into small pieces and add them in. Pour the dressing over everything and fold gently to combine.
Chill and serve. You can serve it right away, but it's even better after an hour or two in the fridge once the flavors have had time to come together. Taste again before serving and adjust the seasoning if needed.