In a large mixing bowl, combine the warm water and active dry yeast. Allow it to sit for about 5-10 minutes until it becomes frothy.
Once the yeast is activated, add the melted butter, 4 tablespoons of sugar, milk, salt, vanilla extract, and eggs. Whisk everything together until well combined.
Gradually add the all-purpose flour to the wet mixture, stirring until a dough forms. Knead the dough until it is smooth and elastic, about 5-7 minutes.
Cover the bowl with a clean kitchen towel and let the dough rise in a warm area for about 1 hour, or until it has doubled in size.
Once the dough has risen, punch it down and divide it into smaller portions. Roll each piece into an oval shape about 1/4 inch thick.
In a deep frying pan or deep fryer, heat the vegetable oil over medium heat. Test if the oil is ready by dropping in a small piece of dough.
Fry each oval of dough for about 1-2 minutes on each side, or until they are golden brown. Use a slotted spoon to remove them from the oil and place them on paper towels to drain.
In a bowl, mix together the 2 cups of sugar and 2 tablespoons of cinnamon. Dust the warm Beaver Tails generously with the cinnamon-sugar mixture.
