In a 10-inch nonstick pan, heat the clarified butter over medium-high heat.
Mix together the grated potato, thyme and garlic in a bowl. Add to the pan of hot butter and spread evenly, about the thickness of a pancake. Reduce the heat to medium and allow to cook until crispy and deeply golden brown, 8 to 10 minutes. Season with salt and pepper.
Flip the potato cake over and continue to cook on the other side, about another 5 minutes. Drain on a rack, then cut into sixths and serve.