In a small bowl, combine the dry baking yeast, warm water, and 2 tablespoons of sugar. Let it sit for about 10 minutes until it becomes frothy.

In a large mixing bowl, combine the ground corn, sea salt, and crushed anise. Mix well.

Add the activated yeast mixture to the corn mixture along with the flour, beer, and pureed butternut squash. Stir until combined and form a sticky dough.

Remove the dough from the bowl and knead it on a floured surface for about 8–10 minutes until it becomes smooth and elastic.

Place the dough in a greased bowl, cover it with a cloth, and allow it to rise in a warm place for about 1 hour or until doubled in size.

Once the dough has risen, punch it down to remove any air bubbles. Shape the dough into rings, about the size of your palm, and create a hole in the center.

Heat oil in a deep pan or fryer to 350°F (175°C). Carefully fry the doughnuts in batches until they are golden brown on both sides, about 3–4 minutes per side.

Remove the picarones from the oil and place them on a paper towel-lined plate to drain excess oil.

In a saucepan, combine brown sugar, water, and lemon or orange peel shreds. Bring to a boil and simmer until it thickens into a syrup.

Serve the picarones warm with the syrup drizzled over them or on the side for dipping.