In a large bowl, stir together the yeast, warm water and the pinch of sugar. Let stand until it is slightly foamy (5 minutes). Then add the other 1/3 cup of sugar, milk, vanilla, eggs oil and salt. Stir it all until it is smooth. Mix in about half of the flour and continue stirring it. Gradually add more flour.
Turn the dough onto a floured surface when it is firm enough. Knead for approximately 6-8 minutes. Add more flour if you need it to form a firm elastic dough. Place dough in a greased bowl and cover,
Let dough sit covered until it rises and doubles (approximately 35-45 minutes). Lightly deflate the dough and pinch off a piece the size of a golf ball. On a floured surface use a rolling pin to roll out the small ball of dough into an oval shape. Put it aside and cover it with a tea towel while you continue to do the same with the remaining dough.
Heat approximately 4 inches of oil in either a deep-fryer, (375 degrees) wok or a Dutch oven. Before placing the flattened dough in the oil, stretch them into ovals and thin them and enlarge them (to resemble the tail). Place the tails in the oil one at a time. Fry in the oil, turn them once until the tails are deep brown. This process usually takes about 1 to 2 minutes per side. Carefully remove the tail from the oil and let it drain on a paper towel. Place left over sugar in a large bowl and add the cinnamon. Toss the beaver tail into the bowl while it is still hot. Shake off any extra sugar and cinnamon mixture.