Cook vegetables: Place whole potatoes (skin-on) and carrots in a pot and cover with cold water. Season the water generously with salt. Bring to a boil and cook 15–20 minutes total, until both are just tender (carrots will cook about 10–15 minutes). Drain, cool slightly, peel, and dice both small.
Cook peas: In the same boiling water, add frozen peas and cook 2–3 minutes, until bright green and tender. Drain and rinse under cold water to cool.
Cook eggs: Place eggs in a small pot, cover with cold water, bring to a boil, then reduce heat and simmer 9–10 minutes. Transfer to cold water, cool, peel, and dice.
Make dressing: Mix mayonnaise with 2–3 tablespoons brine, ½ teaspoon Dijon mustard, black pepper, and a pinch of salt.
Combine: Add potatoes, carrots, peas, eggs, ham, pickles, and green onions. Gently fold.
Chill: Taste and adjust with more brine, salt, or pepper if needed. Chill 1-2 hours (or overnight).
Serve cold and enjoy!
Want a little extra bite? Feel free to add a small amount of finely diced white or red onion to the salad — it adds a sharp, savory kick that a lot of people love in their Olivier. If raw onion feels too strong, soak the diced pieces in cold water for 10 minutes first, then drain before adding.