Roasting sweet potatoes directly on the oven rack allows their skins to become extra-crisp. For a variation, try pale-fleshed Japanese sweet potatoes, which have a richer flavor and are in season in November.
Preheat oven to 400 degrees with racks in upper and lower thirds. Prick potatoes all over with a fork. Rub with 2 tablespoons oil; season with kosher salt. Place directly on top rack, with a parchment-lined rimmed baking sheet on rack below. Roast 45 minutes.
Meanwhile, toss broccoli rabe with remaining 1 tablespoon oil; season with kosher salt and pepper. Carefully remove parchment from lower baking sheet; add broccoli rabe in a single layer. Roast, tossing once, until tender and bright green and potatoes are soft and oozing, 15 minutes. Transfer vegetables to a cutting board; let cool slightly, then chop broccoli rabe into bite-size pieces. Split sweet potatoes open; mash lightly with a fork. Top with broccoli rabe, beans, and pepperoncini. Serve, drizzled with oil and brine and sprinkled with flaky salt.