Make ahead: Cook the potatoes with skin on and let them cool completely, ideally overnight. Let the peas thaw at room temperature. Peel the carrot and cook it shortly in boiling water for about 5 minutes. Then cool it in cold water to stop the cooking process. The carrots get a beautiful color and remain slightly crunchy to the bite, not mushy.
Peel the cooked potatoes and cut them into small cubes. Finely chop the ham, carrots, and pickles. Transfer them to a mixing bowl. Add thawed peas.
Prepare the dressing: In a bowl, put mayo, pickle juice, mustard, sugar, salt, and ground pepper. Stir well until combined.
Pour the dressing over the prepared ingredients. Mix everything together. Let it rest in the fridge for at least an hour.