In the stand mixer mix together the water, milk and pinch of sugar, sprinkle the yeast on top and let sit for 5-10 minutes. Add the egg yolk, oil, remaining sugar, salt and vanilla and stir to combine. Add the flour and knead for approximately 5-6 minutes until combined.
Move the dough to a lightly floured flat surface and form into a ball. Place in a lightly oiled bowl, cover with plastic wrap, place in a warm draft free area and let rise until doubled.
Punch the dough down and knead a few times, divide into 4 parts and form each into an oval shape ¼ inch shape.
Heat 2 inches of oil in a medium heavy pot (or follow the directions if using a deep fryer) using a candy thermometer until temperature reaches 360-370F (180-185C).
Place cinnamon and sugar on a plate.
Fry the dough until golden 1-2 minutes on each side, drain on a paper towel, while still warm press dough gently in the sugar. Shake off any excess. Serve immediately. Enjoy!
Notes
If sugar doesn't stick brush the beaver tail with melted butter then dip in the sugar.While these pastries are best fresh, if you have extras, keep them in an airtight container at room temperature for up to 1 day. Reheat briefly in the oven to crisp them back up.To freeze - they should be completely cooled, place the fried pastries (without cinnamon sugar coating) in a freezer-safe bag or container. Freeze for up to 1 month. Reheat from frozen in a 350°F oven until warmed through. (They won’t be quite as crisp as fresh, but still tasty.) After reheating, coat in cinnamon sugar.