Add the instant dry yeast and granulated sugar to the warm milk in a large bowl. Whisk thoroughly and let rest 15 to 20 minutes, until a foamy layer develops on top.

Add the rest of the warmed milk to the yeast mixture. Gradually add the melted vegetable shortening while continuing to whisk. Add in the granulated and brown sugars, whisking until completely dissolved.

Stir in the beaten eggs, anise seeds, and vanilla extract. Mix the components together and stir until blended and smooth.

Add the flour and salt to the bowl. Using a wooden spoon, mix until a ragged, sticky dough forms.

Dump the dough out onto a floured surface. Work it hard, 12 to 16 minutes or so, until elastic and smooth. Form the kneaded dough into a ball.

Coat a large bowl lightly with cooking spray. Put the dough in, cover it with a clean towel or plastic wrap, and let it rise in a warm place for 1 to 3 hours, or until it has doubled in size.

After rising, punch down dough on floured surface to remove large air pockets. Cut into 10 to 12 equal pieces; roll each piece into a round ball.

Preheat the oven to 390°F (200°C). Prepare two baking sheets with parchment paper or silicone mats. Place one dough ball every 5 inches, 5 to 6 dough balls per tray. Lightly press each ball slightly flat with your hand.

Drape the trays with clean towels and let the buns proof for another 15 to 20 minutes. Just before baking, lightly dust the tops with flour.

Bake the trays one at a time in the middle rack for 10 to 15 minutes, or until the tops and bottoms are evenly golden. Take out of the oven and let it cool before serving.