Bring one large and one medium pot of water to a boil. Cook the potatoes in the large pot until fork tender, 5-7 minutes. Fill a small bowl with ice water and set aside.
Add a teaspoon of salt to the medium pot, and add the fava beans. Turn down the heat and simmer at a gentle boil for 1 minute. Drain immediately and pour the beans into the ice water to stop the cooking process.
Drain and gently squeeze the beans from the waxy outer skin. Drain the potatoes and set aside.
Using a mandoline or sharp chef’s knife, shave the fennel into thin rounds.
In a large mixing bowl, whisk together the mayonnaise, vinegar and mustard. While continuing to whisk, slowly drizzle in the olive oil until emulsified. Add the fennel fronds and season with sea salt and pepper, to taste.
When potatoes are cool enough to handle, cut into halves or quarters. Combine the potatoes, fava beans and fennel with the dressing, season with sea salt and pepper. Can be served warm or cooled in the fridge.