Cook potatoes in their skins. Scrub the potatoes and place in a saucepan with cold water to cover. Bring to a boil, then simmer gently for approximately 20–30 minutes, depending on size, until a small knife enters easily but the potatoes remain intact. Drain. Allow additional time for the water to heat; do not force a 25-minute finish if the centers are still firm.
Cook carrots, then peas. While the potatoes cook, cut peeled carrots into ¼-inch (5–7-mm) dice. Bring another pot of water to a boil and add the measured cooking-water salt. Cook carrots for about 6–8 minutes until tender but still holding their shape, then lift out with a slotted spoon and drain well. Return the water to a boil, add the frozen peas, and cook separately for about 2–4 minutes, or as their package directs. Drain thoroughly.
Hard-boil and cool the eggs. Put the eggs in a separate saucepan, cover with cold water, and bring to a clear boil. Cook for about 9–10 minutes as a starting guide, until yolks and whites are fully firm; larger eggs may need longer. Transfer immediately to cold or ice water, cool, peel, and refrigerate until assembly.
Chill the cooked ingredients promptly. Spread drained vegetables in shallow containers rather than leaving them in hot pots or a deep pile. Let heavy steam escape briefly and refrigerate promptly; small warm portions can go into the refrigerator. Allow about 60 minutes as an ingredient-cooling estimate, including at least 30 minutes refrigerated for the potatoes, and wait until all components are at 40°F (4°C) or below before dressing. Cooling can take longer. Refrigerate within 2 hours of cooking, or 1 hour above 90°F (32°C); never wait hours on the counter for room temperature.
Drain pickles and dice cold ingredients. Drain the pickles before weighing, cut into ¼-inch (5–7-mm) dice, and drain the cut pieces again for a few minutes. Blot if very wet. Peel the completely cold potatoes and dice to match; chop the cold hard-boiled eggs into similar small pieces. Cut gently so the potatoes do not mash.
Whisk the dressing. Whisk the mayonnaise and cold cultured sour cream together in a small bowl. Add the measured mustard and lemon juice and whisk smooth. Mix in the pepper and initial dressing salt. Taste with a clean spoon, remembering that pickles, mayonnaise, and mustard already contain salt. Keep the dressing cold.
Fold without crushing. Loosely combine the cold potatoes, carrots, peas, and drained pickles. Add the chopped eggs. Fold in approximately three-quarters of the dressing with a large spoon or flexible spatula, then incorporate the rest gradually. Mix only until evenly coated; do not beat or mash the potato cubes.
Chill the assembled salad. Transfer to shallow covered containers and refrigerate for at least 2 hours at 40°F (4°C) or below. For larger batches, use additional containers with space around them rather than one deep bowl. Preparing the salad the day before serving is practical; the cooling intervals are not automatically multiplied when scaling.
Adjust and serve cold. Fold gently once more and taste just before serving. Add a little of the optional extra salt only if needed; any further pepper or lemon adjustment is outside the measured base formula. Serve a small bowl at a time, keeping the rest refrigerated. Return safely handled portions promptly to cold storage and discard food left unrefrigerated beyond 2 hours, or 1 hour above 90°F (32°C). Chilling again does not reset that limit.