Melt the butter in a small saucepan over low heat. Add the milk and set aside so the mixture is lukewarm.
In a stand mixer fitted with the dough hook attachment, combine the flour, sugar, yeast, and anise seeds. Add the melted butter and milk mixture. Knead on medium-low for 10 minutes.
Transfer the dough to a lightly buttered bowl, cover with a tea towel, and let rise in a warm spot for about 1 hour, or until doubled in size.
Once the dough has doubled in size, preheat the oven to 425ºF (220ºC). Line a baking sheet with parchment paper.
Divide the dough into 12 equal pieces. On a clean surface, roll out each piece of dough into a long and thin rope, about 18 inches (45 cm) long.
Form each dough rope into a U-shape, then twist the ends together. Bring the twisted ends back down over the bottom of the U-shape and press down to form a pretzel shape.
Place on the prepared baking sheet, cover with a tea towel, and let rise for 30 minutes.
Brush the tops of the pretzels with the beaten egg and sprinkle with anise seeds.
Bake for about 15 minutes, or until golden brown. Transfer to a wire rack to cool.
