Preheat the oven to 425 degrees F. Line a rimmed baking sheet with aluminum foil.
Combine the potatoes, fennel, olive oil, salt and pepper in a large bowl. Spread the mixture in a single layer on the prepared baking sheet. Bake until the potatoes are tender and lightly browned, about 25 minutes. Cool, about 30 minutes.
Combine the mayonnaise, chives and parsley in a large bowl. Add the cooled potato mixture, tossing gently to combine. Serve immediately, or cover and chill up to 3 days.