Peel the potatoes and drop them in a bowl of cold water to keep them from turning brown.,

Using the small julienne blade of a mandoline, cut the potatoes lengthwise in long matchsticks.,

Place the potatoes on a clean kitchen towel and squeeze the towel to dry the potatoes without breaking them up.,

Place the potatoes in a bowl and toss them with 1 teaspoon salt and ½ teaspoon pepper.,

Heat 2 tablespoons oil in a small (8-inch) sauté pan with sloped sides over medium heat.,

Add all the potatoes to the pan and arrange them so they lie flat (the pan will be very full!). Press them lightly with a metal spatula.,

Allow the potatoes to cook undisturbed for 5 minutes.,

Drizzle 1 tablespoon oil down the sides of the pan around the galette and cook for another 5 minutes.,

When the galette is nicely browned on the bottom, loosen it carefully around the edge with a large, narrow, flexible metal spatula and flip it over with a large flat spatula. (Be careful! The oil in the pan is very hot!),

Cook the galette for 2 minutes.,

With the tip of a knife, run the pat of butter around the edges of the galette, allowing it to melt down the sides.,

Continue to cook for 4 to 5 minutes, until nicely browned on the second side.,

With the large flat spatula, transfer the galette to a paper towel and allow it to sit for 30 seconds.,

Transfer to a board and cut in quarters with a large chef’s knife.,

Transfer to a plate, sprinkle with chives and fleur de sel, and serve hot.