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1
Make the syrup. Combine water, orange peel strips, and piloncillo in a small saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves. Continue boiling without stirring until the syrup reaches the thin-thread stage, 106–110°C (223–230°F). Remove the orange peel.
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2
Incorporate the fats. Remove the pan from heat. Stir in the vegetable shortening and lard until both melt fully into the syrup. Transfer to a large mixing bowl and allow to cool until the mixture is warm but not hot — roughly 40–45°C (104–113°F).
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3
Build the dough. Stir the baking powder, baking soda, and salt into the cooled mixture. Add the lime juice and beaten eggs, mixing well. Add the flour in two or three additions, stirring after each, until a stiff, cohesive dough forms. Knead briefly in the bowl until smooth. Do not add water.
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4
Rest. Wrap the dough and let it rest at room temperature for 15 minutes.
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5
Roll and cut. Heat the oven to 175°C (350°F). Line two baking sheets with parchment. On a lightly floured surface, roll the dough to 6 mm (1/4 inch) thickness. Cut into star or flower shapes with a 6–7 cm cutter. Transfer to prepared sheets.
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6
Glaze and sugar. Whisk the egg yolk with the milk. Brush the surface of each cookie lightly. Sprinkle generously with granulated sugar.
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7
Bake. Bake for 25–35 minutes, rotating the sheets once halfway through, until the cookies are a pale golden brown and feel firm and dry throughout. They will crisp further as they cool.
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8
Cool. Transfer to a wire rack. Store in an airtight tin for up to two weeks.