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1
Combine the piloncillo, water, and vinegar in a saucepan and bring to a boil over high heat.
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2
Lower the heat and continue cooking until the piloncillo has dissolved and the mixture reaches a honey-like consistency.
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3
Set aside.
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4
Cream together the butter and sugar with an electric mixer or in a bowl with a wooden spoon.
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5
In a separate bowl, combine the flour and salt, then add to the butter mixture gradually and beat until a uniform dough is formed.
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6
Cover with plastic wrap and let rest for 10 minutes at room temperature.
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7
Meanwhile, heat the oil in a heavy, deep pan over medium heat to 375F.
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8
Turn the dough out onto a lightly floured surface and roll out into a square or rectangle about 1/8 inch thick.
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9
Cut into 1-inch squares.
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10
Fry the dough in batches until lightly golden, 3 to 5 minutes.
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11
Transfer with a slotted spoon to a paper bag or paper towel to drain.
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12
Repeat until all the dough is fried.
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13
Put the drained fried dough in the syrup and stir well to coat all the squares.
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14
Once coated, take them out with a slotted spoon or spider and place 6 to 8 mounds on a wire rack.
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15
Carefully press together with your hands to form balls (this can be a sticky situation, so you may want to wear gloves).
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16
Allow the mueganos to set for 5 minutes before serving.