1. Remove the fennel fronds, coarsely chop and set aside. Remove the tough outer layer of the fennel bulbs, then halve each bulb lengthwise and core. Using a mandoline or sharp knife, thinly slice 1½ fennel bulbs lengthwise. Finely dice the remaining half bulb.

2. Cut 1 of the lemons into half-moons. Discard the seeds. Juice the remaining lemon and set aside.

3. Heat the broiler with an oven rack 4 to 5 inches from the flame. Toss together the sliced fennel, sliced lemon, and 1 tablespoon of the olive oil on a parchment-lined baking sheet. Season with salt and spread the fennel and lemon slices in a single layer. Broil, shaking the baking sheet once or twice, until the fennel is tender and lightly charred in spots, 3 to 5 minutes.

4. Toss the cooked beans with the broiled fennel and lemon, the raw fennel, the remaining 2 tablespoons of olive oil, the olives, 2 tablespoons lemon juice (or to taste), red pepper flakes and fennel fronds. Season with salt and pepper. (The salad will keep in an airtight container in the refrigerator for up to 3 days.) Serve warm, cold or at room temperature.