Puntarelle stays bright and crisp in this salad, while beets bring a tender, earthy sweetness. Puntarelle is a specialty buy—check your local farmers market, or substitute another bitter chicory.
Preheat oven to 375°F. Drizzle beets with 2 tablespoons oil on a large rimmed baking sheet; toss to coat, and arrange beets in an even layer. Roast in preheated oven until beets are fork-tender, 30 to 40 minutes. Let cool 15 minutes. Rub beets between paper towels to remove skins; discard skins. Cut beets into halves or quarters; transfer to a medium bowl. Stir in 1 tablespoon oil and 1/4 teaspoon salt; set aside.
While beets roast, cut 1 lemon in half crosswise; remove and discard seeds. Finely chop lemon. Place chopped lemon in a small bowl; stir in remaining 2 teaspoons salt. Let stand 15 minutes. Stir in garlic, honey, mustard, pepper, and remaining 1/2 cup oil. Juice remaining lemon to equal 1/4 cup; discard squeezed lemon. Stir 2 tablespoons lemon juice into chopped lemon mixture; reserve remaining 2 tablespoons lemon juice. Set aside.
Remove and discard outer leaves of puntarelle, reserving a few smaller leaves for serving. Separate the puntarelle head into individual stalks by slicing off each individual stalk from the inner core. Slice each puntarelle stalk in half lengthwise. Thinly slice each puntarelle half crosswise into 2- to 3-inch strips. Place puntarelle strips in a bowl filled with ice water; stir in reserved 2 tablespoons lemon juice. Let soak 1 hour. Drain and pat dry. Transfer to a dry large bowl.
Add parsley, dill, mint, tarragon, reserved outer puntarelle leaves, and 2 tablespoons chopped lemon dressing to puntarelle in bowl; toss to combine.
To serve, divide citrus segments and roasted beets evenly among 4 plates. Top evenly with mounds of puntarelle mixture. Drizzle desired amount of remaining chopped lemon dressing over exposed outer edges of citrus and beets. Sprinkle with ricotta salata.
Puntarelle can be soaked and drained 1 day ahead; refrigerate in an airtight container.