In a medium saucepan, combine the water, piloncillo stick, cinnamon stick, orange zest, and extract. Cook over medium-high heat, stirring occassionally, until the piloncillo stick dissolves. Reduce the heat to medium-low heat and simmer steadily until the mixture has reduced to 1 cup, about 30 minutes.

Remove from the heat, strain into a small bowl, and set aside.

In a medium bowl, whisk together the flour, 1 tablespoon sugar, baking powder, salt, and 1/4 teaspoon cinnamon. Form in well in the center and add the egg and 1 tablespoon oil. Stir until the mixture resembles a coarse meal. Slowly add the warm water, a tablespoon at a time, mixing and kneading with hands until a soft and smooth dough forms. Cover the dough and let rest for 30 minutes.

Divide the dough into 12 small balls and cover.

Heat 1 inch of oil in a large skillet to 350°-375°.

Place one dough ball on a lightly floured surface and roll to form a circle as thin as possible without tearing. Place on a large dish towel. Repeat with the remaining dough balls, placing them on the dish towel, but not touching each other.

Line a baking sheet with paper towels.

Fry the dough rounds one at a time, pressing down with a spatula to submerge the dough so large bubbles do not form, until golden and crispy, about 1 minute on each side. Drain on the paper towels and let cool.