Preheat the oven to 200°C (400°F). Grease a 12-hole muffin tin lightly with olive oil or line with parchment circles.
Wash and thinly slice the potatoes and sweet potatoes into rounds, about 2mm thick. A mandolin works best for uniform slices.
In a large bowl, toss the potato slices with the wild garlic oil until well coated. Season with salt and pepper.
Stack the slices into the muffin tin holes, layering them evenly and slightly overlapping. Overfill each hole, as the stacks will shrink as they bake. Insert a cocktail stick or wooden skewer into each potato tower to make them easier to serve.
Bake in the oven for 45–50 minutes, or until the tops are golden brown and crispy, and the centres are tender when pierced with a knife.
Allow to cool for 5 minutes before carefully removing with a spoon or small offset spatula.
Serve warm as a side or savory snack.