4 scalloped potatoes with caramelized Recipes

unsalted butter, room temperature, divided, extra-virgin olive oil, fennel bulbs (about 1 1/2 lb), trimmed, quartered, cored, thinly sliced (about 6 cups), kosher salt , freshly ground pepper, dry white wine or dry vermouth, bay leaves, waxy potatoes (such as yukon gold), peeled, sliced 1/8 thick, heavy cream, whole milk, garlic clove, halved, shredded comte or gruyere

unsalted butter, shallots, peeled, thinly sliced, russet potatoes, fresh thyme leave, salt, pepper, heavy cream or 2 cups half-and-half, shredded gruyere cheese

slender sweet potatoes (1 1/2 lb), vegetable oil, salt and freshly ground pepper, onion, thinly sliced