Stir together the warm water, warm milk, yeast and 1 teaspoon of sugar in the bowl of a stand mixer. Let sit for about 10 minutes or until foamy. Stir in the melted cannabis butter, sugar, salt, vanilla and egg. With the dough hook on the mixer, add flour and mix until the dough comes together and no longer sticks to the sides of the bowl. Increase mixer speed to knead dough for about 5 minutes until the dough is smooth and elastic. If dough is sticky, add a little extra flour.
Transfer dough to a lightly oiled bowl and cover with a clean kitchen towel. Let rise until doubled in size, about 1 hour.
Punch down dough and transfer to a lightly floured surface. Cut into 8 equal sized pieces and shape each piece into an oblong.
Use a rolling pin to flatten and roll out each piece of dough into an oval. Use a knife to score a crisscross pattern in the top of dough. Transfer donuts to a lightly floured baking sheet, cover with a kitchen towel, and let rise for 30 minutes.
Mix cinnamon and sugar together in a large bowl. Set aside.
Add about 2-inches of oil to a large skillet and heat to 350°F or until a small bit of dough dropped in the oil floats to the surface sizzling. Keep an eye on the oil during the cooking process and be sure to lower the temperature if you see it smoking. Fry Beaver tails for about 30 seconds per side, or until golden brown. Remove to the bowl of cinnamon/sugar and turn to coat. Serve immediately.