Bloom Yeast: Combine warm milk and active dry yeast in a bowl; let it sit undisturbed for about 8 minutes.

Mix Wet Ingredients: Add light brown sugar, canola oil, melted butter, salt, and vanilla extract into the bloomed yeast. Whisk everything until well combined, then gently mix in the egg.

Incorporate Dry Ingredients: Gradually sift in the all-purpose flour while mixing, stirring until a soft dough begins to form.

Knead Dough: Transfer the dough to a floured surface and knead it for about 5 minutes until it becomes smooth and elastic.

First Rise: Cover the dough and let it rise in a warm place until it has doubled in size, around 45 minutes.

Prepare Oil: Heat enough canola oil in a heavy pot to reach 355-365°F.

Shape Dough: Punch down the risen dough and cut it into 12 equal pieces. Shape each piece into oblong shapes.

Fry Tails: Gently drop each shaped dough into the hot oil, frying for 30-60 seconds on each side until golden brown.

Cinnamon Sugar Coating: Remove them and coat immediately in a mixture of cinnamon and granulated sugar.

Cooling: Place the coated beaver tails on wire racks to cool slightly before serving.