3 tablespoons unsalted butter
15 cups sliced yellow onion (about 4 pounds)
3/4 teaspoon black pepper
1 Honeycrisp or Pink Lady apple, peeled, quartered, and cut into julienne strips
3 thyme sprigs
2 bay leaves
1/2 cup Madeira wine or dry sherry
6 cups lower-sodium beef broth
1/2 cup apple cider
1 tablespoon sherry vinegar
10 (1/2-ounce) slices sourdough bread, cut into 1-inch cubes
2 cups (8 ounces) grated Gruyère or Swiss cheese
Thyme leaves (optional)