Preheat oven to 375 degrees F. In a small saucepan heat 3 tablespoons of the butter over medium heat until light brown, about 7 minutes; remove from heat.
Arrange half of the fennel and half of the celery in a 2 quart baking dish. Top with half of the onion slices. Sprinkle with 1/2 cup of the cheese. Repeat layers. In the saucepan whisk together browned butter, cream, the 2 tablespoons dill, the salt, and pepper. Drizzle over vegetables. Cover baking dish tightly with foil. Bake for 45 minutes.
Meanwhile, in a small microwave-safe bowl, microwave the remaining butter until melted. Add bread crumbs and nuts; toss to coat.
Uncover baking dish; sprinkle the remaining cheese and the bread crumb mixture over vegetable mixture. Bake, uncovered, for 30 to 35 minutes more or until vegetables are tender and crumbs are golden. Let stand for 15 minutes before serving. Top with dill sprigs.