1. Put the carrot, onion, daikon, and garlic in a food processor. Pulse until diced small. In a large bowl, season the duck legs with salt, then cover with the vegetable mixture and five-spice powder. Cover and marinate in the refrigerator overnight.

2. Preheat the oven to 200°F. Put the duck legs in a roasting pan, skin side up, and cook for 8 hours, or until very soft. Remove from the oven, cool slightly, then remove the skin and bones, reserving the rendered fat. Mix ¼ cup of the reserved fat with the oil, duck meat, scallions, pickled ginger, and soy sauce.

3. Put an eighth of the duck meat mixture in a line lengthwise in the center of an egg roll wrapper. Brush a little egg wash around the edges of the wrapper. Fold in the sides; then, starting from one end, roll up tightly. Repeat with remaining wrappers and filling.

4. Pour oil to a depth of at least 1 inch in a heavy, deep saucepan and heat to 350°F. Add the duck sticks and cook until golden brown and crisp, turning occasionally for even browning. Do not overcrowd; work in batches if necessary. Drain on paper towels and serve.