Step 1In a small saucepan, combine the whole piloncillo with the water, cinnamon stick, cloves, lime zest and orange zest. Cover and cook over medium heat, turning and tapping the piloncillo occasionally with a wooden spoon, until the mixture comes to a boil, about 5 minutes. Reduce the heat to low and continue to cook, covered, until the piloncillo dissolves, about 6 minutes.
Step 2Uncover and continue cooking until the syrup is thick enough to lightly coat a spoon, an additional 10 minutes. Leave the spices and citrus zests in the syrup. This makes about 1 cup syrup, which will keep up to 2 weeks, covered and refrigerated. Bring to room temperature before serving, straining if desired.
Step 1Heat the oven to 400 degrees. Put the sweet potatoes in a roasting pan in which they fit in one layer, rub them with vegetable oil, and roast them until they feel soft when squeezed and can easily be pierced with a fork, 45 minutes to an hour (timing will depend on the size of the potatoes). Rotate the potatoes occasionally for even roasting. Set aside until they are just cool enough to handle.
Step 2Peel the sweet potatoes while they are still warm, then cut them into large chunks and mash them to a smooth purée (you will need 2¼ cups purée; any extra can be saved for another use).
Step 3Put the mashed sweet potatoes in a small saucepan. Cut 2 tablespoons of the butter into 4 pieces and add to the pan. Stir in the milk, one-fourth teaspoon salt, 2 teaspoons sugar and the cinnamon. Cook over medium-low heat, stirring frequently, until the milk and butter are absorbed, about 2 minutes. Remove from the heat and set aside to cool.
Step 4Make choux pastry: Cut the remaining butter into 4 pieces and put them in a small saucepan. Add the water and the remaining salt. Heat over low heat until the butter melts, then increase the heat to medium-high and bring to a boil. Remove from heat, immediately add the flour all at once, stirring vigorously with a wooden spoon until the mixture is smooth. Set the pan over low heat and beat the mixture for about 30 seconds, then remove from heat and set aside to cool for 5 minutes. Add 1 egg and beat it quickly and thoroughly into the mixture; it will look separated at first, but keep beating until the egg is completely incorporated and the mixture is smooth. Then beat in the second egg. Transfer the dough to a bowl.
Step 5Add the sweet potato purée in three portions to the dough, beating after each addition until the mixture is smooth and thoroughly blended. Line trays or plates with paper towels.
Step 6Fill a wide, heavy pot with oil to a depth of about 4 inches, and heat the oil until it reaches about 350 degrees. If a thermometer is not available, test by putting a scant teaspoon of sweet potato mixture into the oil; when the oil is hot enough, it should bubble vigorously around the batter.
Step 7Take a small, mounded spoonful of batter and use a second spoon to slide it gently into the oil, forming a rounded fritter. Do not crowd the pan because the fritters need room to puff. Fry the fritters over medium to medium-high heat until they are deep golden brown on all sides and set in the center, about 3 minutes (timing will vary depending on the size of the fritters and the temperature of the batter and oil). While frying, turn the fritters over if needed. If the fritters darken too quickly before they are completely set, reduce the temperature of the oil. The cooked fritters will be crisp but very tender.
Step 8Transfer the fritters to the paper towel-lined trays. Serve the fritters while they are still warm, drizzled with syrup. Serve the remaining syrup separately.