Step 1

Heat oil in a large heavy skillet, preferably cast iron, over medium. Add potatoes and season with salt and pepper. Cook, tossing occasionally, until potatoes are golden brown all over, 10–12 minutes.

Step 2

Add butter, 2 Tbsp. lime juice, 2 tsp. piment d’Espelette, and ½ cup water to skillet. Cover, reduce heat to low, and cook, tossing occasionally, until potatoes are fork-tender and no liquid remains, 10–12 minutes. Remove from heat and stir in remaining 1 Tbsp. lime juice. Taste and season with more salt and pepper if needed.

Step 3

Transfer potatoes to a platter and blanket with cheese. Dust generously with more piment d’Espelette.