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Start by weighing your flour or measuring it by gently spooning it into a cup, then sweeping off any excess. In a large bowl or the bowl of a stand mixer fitted with the flat beater, combine the flour, salt, baking powder, and baking soda.
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In a medium saucepan with high sides, combine the piloncillo, water, anise seeds, and cinnamon. Bring to a simmer over medium heat. Adjust the heat to maintain a slow simmer, stirring regularly with a flexible spatula until most of the piloncillo dissolves and a thick syrup the consistency of molasses forms, about 20 minutes. The syrup should measure between 250°F and 255°F on a digital thermometer.
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Remove the pot from the stove and carefully remove the cinnamon stick, if using. Stir in the honey until fully incorporated. Then stir in the butter until melted. (The butter will not fully incorporate; that’s OK.)
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Create a well in the center of the dry ingredients and add the piloncillo mixture. Mix on low speed until well combined.
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Add the eggs one at a time, stirring to combine the first before adding the second. The mixture will be sticky and seem more like thick batter than dough.
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Transfer the dough to a sheet of plastic wrap or your favorite reusable wrap. Shape the dough into a large oval about 9" x 10" and wrap to seal. Refrigerate the dough for at least 3 hours or overnight.
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Once the dough has chilled, preheat the oven to 350°F with the rack in the center position. Line 3 baking sheets with parchment or silicone mats, or lightly grease.
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Flour your work surface generously and divide the dough into 4 pieces. Working with 1 piece of dough at a time (return the other 3 pieces to the refrigerator), roll the dough to about 1/4" thick, adding more flour as needed to prevent sticking. If the dough begins to crack, that’s OK; simply press or pinch it back together.
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Using a 3 3/4" to 4" pig-shaped cookie cutter that has been dipped in flour, cut the dough into cookies. Transfer the cookies to a baking sheet as you go, spacing them about 1" apart. Re-roll the dough scraps and cut out additional cookies until all the dough from the first piece is used.
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Brush the puerquitos with egg wash and bake for 12 to 14 minutes, or until evenly puffed all over and slightly firm to the touch. Allow them to cool on the pan for about 5 minutes before transferring them to a rack to cool completely.
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While the first tray bakes, work with another piece of dough to fill the second baking sheet with cookies. Continue until all the dough is used, baking one tray of cookies at a time.
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Storage information: Serve puerquitos at room temperature; store leftover puerquitos in an airtight container at room temperature for up to 4 days.
