1. Place the trotters in a large pot with the carrots, celery, onion, bay leaves, thyme, 1 teaspoon salt and peppercorns. Cover with water and simmer until very tender, 3 to 4 hours. Remove the trotters from the broth. Strain the broth, reserving the broth and vegetables separately. Save the broth for future use.
2. Preheat the oven to 400 degrees F. Scatter the reserved cooked vegetables around the bottom of a roasting pan. Place a rack over the vegetables and arrange the trotters, skin side down.
3. To make the breadcrumbs, heat the butter and oil in a large skillet over medium heat. Add the garlic and cook until slightly golden, about 1 minute. Add the breadcrumbs, parsley, sage, 1 teaspoon salt and freshly ground pepper to taste. Cook until the breadcrumbs are toasted and fragrant, stirring occasionally, about 3 minutes.
4. Press the breadcrumbs on top of the trotters. Roast until the breadcrumbs are golden and very crisp, 20 to 30 minutes.
5. Serve with whole grain or Dijon mustard on the side if desired.
For a make-ahead recipe, cook the trotters in the stock the day before. Cool and store in the broth. The next day, skim the broth and gently reheat until it is liquefied. Remove the trotters and continue with the recipe as written. Before placing in the oven, cover the roasting pan with foil and bake until the trotters are hot through, about 30 minutes. Uncover and cook until the breadcrumbs and browned and crispy.