How to Make It
Preheat oven to 375°F. Shred potatoes in a food processor fitted with the shredding attachment. Place shredded potatoes on a clean towel; wring out excess liquid. Place towel with potatoes in a fine wire-mesh strainer inside a bowl; place a small skillet on potatoes to weigh down. Set aside.
Heat oil in a large skillet over medium. Add fennel and onion; cook, stirring often, until tender but not browned, about 10 minutes. Add garlic; cook, stirring constantly, 1 minute. Remove from heat; transfer mixture to a large heatproof bowl.
Grease bottom and sides of a 9-inch round cake pan with 1/4 cup duck fat. Remove potatoes from towel; discard drained potato liquid in bowl. Stir potatoes into fennel mixture. Add eggs, flour, 1/4 cup raisins, salt, pepper, ground fennel seeds (if using), and 1/4 cup duck fat; stir to combine. Spread mixture in prepared cake pan; place on a rimmed baking sheet.
Bake in preheated oven until top of kugel is crispy, about 45 minutes. Remove from oven; let cool in pan completely, about 2 hours.
Preheat oven to 425°F. Spread remaining 1/4 cup duck fat in a rimmed baking sheet. Remove kugel from cake pan. Cut into 12 wedges, and rub cut sides of each kugel wedge in duck fat on baking sheet to coat. Arrange wedges in an even layer on baking sheet.
Bake at 425°F until wedges are crisped and browned on cut sides, about 20 minutes, flipping once after 10 minutes.
Drizzle wedges evenly with vincotto; sprinkle with remaining 1/4 cup raisins. Top each wedge with about 2 tablespoons chicken liver mousse; garnish with basil.