Use a mandoline or a sharp knife to cut potatoes into very thin slices, about ⅛-inch to 16-inch thick. Place in a large bowl.
Combine melted butter, parsley, oregano, thyme and garlic in a glass measuring cup and stir until well mixed. Pour over potatoes, season with salt and pepper and toss to coat the slices evenly.
Layer the potatoes in the muffin tin, stacking them until they are about ½-inch above the edge of each muffin cup (they will shrink down as they cook).
Set on a baking sheet to catch any drips then bake for 40-50 minutes, or until golden brown and crispy on the edges.
Let cool 5 minutes, then run a knife around the potato stacks and carefully remove them from the pan. Garnish with fresh herbs and flaky salt. Serve hot.