Fill an herb sachet bag with fennel seeds, anise seeds, parsley sprigs, thyme sprigs, star anise, and bay leaf.
Discard fennel fronds, and cut fennel bulbs in half through the center. Cut each half into 3 wedges, yielding 6 pieces from each head.
Place wedges in a large saucepan with herb sachet, wine, liqueur, vinegar, and 1/4 cup of the lemon juice; add water to cover fennel. Sprinkle with 1 tablespoon of the salt.
Place a small plate on fennel to submerge fennel in liquid. Bring to a simmer over medium. Cook fennel until tender and translucent, 1 hour to 1 hour and 20 minutes. Remove from heat.
Using a slotted spoon, transfer fennel wedges to a plate lined with paper towels. Reserve 1 cup of the cooking liquid. Let fennel cool to room temperature, about 20 minutes.
Preheat oven to 400°F with oven rack 8 inches from heat. Place reserved 1 cup fennel cooking liquid in a small saucepan over medium-high. Bring to a boil, and cook until reduced to 1/4 cup, about 13 minutes.
Whisk together reduced fennel cooking liquid, lemon zest, olive oil, chopped parsley, chopped anchovies, and remaining 2 tablespoons lemon juice and 3/4 teaspoon salt.
Place fennel in a 9- x 13-inch baking dish; drizzle with vinaigrette, and toss to coat. Evenly sprinkle with breadcrumbs and Parmigiano.
Bake in preheated oven until bubbling, about 25 minutes. Increase temperature to broil. (Do not remove dish from oven.) Broil until top is lightly browned, 4 to 5 minutes.
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