Preheat the oven to 250°F. Butter a 13 x 9 x 2-inch (33 x 22 x 5 cm) baking dish and set aside.
Scatter bead in a single layer on a rimmed baking sheet. Bake, stirring occasionally, until dried out, about 1 hour. Let cool; transfer to a large bowl.
Preheat oven to 350°F (180°C). Melt the bacon fat and butter. Sauté broken up sausage meat for about 5 minutes. Remove with slotted spoon and set aside.
Add onion to skillet, cook for 5 minutes, add carrots and celery and cook for another 5
minutes. Let cool slightly.
Beat eggs and add to broken bread pieces. Add herbs, salt, and pepper. Add vegetables and sausage.
Stir in 3⁄4 cup hot stock. Put mixture into prepared baking dish, drizzle with remaining stock.
Cover with foil and bake for 30 minutes. You can stop here and refrigerate until ready to serve.
If serving, uncover and bake until top is golden, another 10 minutes. If reheating, reheat first covered, then uncover and add some slices of butter and return to oven uncovered for 5 minutes.