Puff pastry is the perfect balance of crunchy and buttery for tarts like this one. Serve this potato-leek tart as a first course or alongside roast turkey instead of mashed potatoes.
Preheat oven to 375°F. Line a baking sheet with parchment paper.
Lay puff pastry flat on the prepared pan. Prick all over with a fork. Fold the sides over to form a 1/2-inch border. Brush with a little water to seal the edges and crimp gently with a fork. Set aside in the refrigerator.
Mix gochujang, honey and oil in a medium bowl. Add hot water and mix until smooth. Set aside 2 tablespoons of the mixture for drizzling. Add leek, potato, salt and pepper to the bowl and toss to coat. Scatter some leek slices over the pastry, then shingle the potatoes and the remaining leek in a single layer within the borders. Sprinkle with sesame seeds.
Bake the tart, rotating the pan from front to back halfway through, until the crust is golden brown all over and the potatoes and leeks are tender when pierced with a knife, 50 to 55 minutes.
Let cool for 5 minutes. Drizzle with the reserved 2 tablespoons sauce and sprinkle with chives. Serve warm or at room temperature.