This bright and tangy potato salad pairs wonderfully with the ham. We prefer buttery Castelvetrano olives if you can find them.
Combine potatoes, water, and 1 tablespoon of the salt in a large saucepan. Bring to a boil over medium-high. Reduce heat to medium-low, and simmer until tender, 8 to 12 minutes. Drain; spread potatoes on a baking sheet in a single layer, and let stand until cool, about 20 minutes.
Chop fennel fronds to equal 1/2 cup. Thinly slice fennel bulb. Toss together chopped fronds, sliced fennel, green olives, oil, lemon juice, and scallions in a large bowl. Add cooled potatoes, pepper, and remaining 1 teaspoon salt; gently stir to combine. Serve at room temperature, or cover and chill up to 1 day.