1. To make the Peking duck: Arrange the duck breasts on a rack over a baking pan, skin side up. 2. Mix the honey, rice vinegar, and soy sauce together in a small bowl and brush over the skin of the duck. Let the duck breasts sit at room temperature for 1 hour, then brush them again and let sit for 15 minutes. 3. Meanwhile, begin making the dough for the pancakes. Combine the flour and water in a large bowl and stir with a wooden spoon. When the dough comes together, turn it out on a lightly floured surface and knead gently for 10 minutes, or until it is smooth and elastic. Divide the dough into 2 pieces, cover it with an inverted bowl or damp towel, and let it rest for 20 minutes. 4. Preheat the oven to 375º. 5. Add 1/2 cup of water to the baking pan with the duck breasts. Bake for 30 minutes or until the skin is crispy and the duck is cooked through. (If the skin isn't crispy enough, run the breasts under the broiler for about 3 minutes.) Remove the duck from the oven and let it rest until it is cool enough to handle, about 15 minutes. 6. While it cools, make the pancakes. On a lightly floured surface, roll out the dough until it is 1/8-inch thick. Cut into 24 rounds using a 2 1/2-inch round cookie cutter. 7. Brush the tops of the half the dough rounds with sesame oil and top with the unbrushed rounds. Roll out the rounds until they are 6 inches in diameter, stack them on a plate, and cover them with a damp towel. Continue with the remaining dough. You can combine any scraps and roll them out one more time before discarding them. 8. To cook the pancakes, heat a skillet over medium heat and add a pancake to the hot pan. Cook about 1 minute, then flip it and cook for 1 minute longer. The pancake will puff up and brown slightly. Gently separate the halves and stack the cooked pancakes on a dish. Cook the remaining pancakes in the same manner. 9. Peel the skin from the cooled duck and cut it into small slices. Carve the duck into thin slices and arrange it on a plate next to the skin. 10. Allow your guests to assemble their own pancakes. Spread about 1 teaspoon of duck sauce down the middle of each pancake. Top with green onion, cucumber, duck, and skin and roll the pancake up. 11. Make ahead: You can freeze cooked pancakes for up to 1 month or hold them in the refrigerator for up to 2 days. Just separate them with a layer of parchment or waxed paper to make peeling them apart easier, cover with plastic, and, if freezing, cover with a layer of aluminum foil. Thaw and reheat in a steamer, or wrapped in foil in a 350º oven for 10 minutes. ---------------------------------------------------------------------------
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