Step 1: Preheat oven to 375°F. Grease a 13- x 9-inch baking dish with butter, and set aside. Place sausage, fennel, onions, and thyme in a single layer on a large rimmed baking sheet. Drizzle with oil, and sprinkle with 1 teaspoon salt and 3/4 teaspoon pepper. Bake in preheated oven until browned and softened, 20 to 25 minutes. Set aside.
Step 2: Place bread in a single layer on a rimmed baking sheet, and bake at 375°F until very lightly toasted and dried out, 15 to 18 minutes. Let cool 5 minutes.
Step 3: Whisk together eggs and chicken stock in a large bowl. Add bread, sausage mixture, remaining 1 1/2 teaspoons salt, and remaining 1/4 teaspoon pepper; stir well. Scrape into prepared baking dish. Cover tightly with aluminum foil; let stand at room temperature 45 minutes.
Step 4: Bake, covered, at 375°F until heated through, about 40 minutes. Uncover and bake until lightly browned, about 30 more minutes. Let stand 10 minutes; garnish with fennel fronds, and serve.