Japanese Potato Salad

Name: Japanese Potato Salad
Ingredients: 5 Yukon Gold potatoes (800g), peeled and cut into 1/2” cubes; 1 large carrot, peeled, quartered lengthwise, then cut into ¼” pieces; 1 Japanese or Lebanese cucumber* (100g), thinly sliced; 1/4 onion (60g), thinly sliced; 1/2 teaspoon salt + 1/2 teaspoon salt; 3 tablespoons mayonnaise (preferably Kewpie); 1 tablespoon rice vinegar or lemon juice; 1 teaspoon sugar or honey; black pepper to taste; 4-5 slices ham (80g), chopped