In a large bowl or the bowl of a stand mixer fitted with the a dough hook, stir together the yeast, 2 tsp honey, and warm water. Let stand 5 minutes. Stir in the warm milk, 3 tbsp honey, butter, salt, vanilla, egg, and oil.
Gradually add in the flour 1/2 cup at at time. Mix and scrap down the sides of the bowl after each addition. After all the flour has been added in, mix until a smooth dough ball forms.
Place the dough ball in the greased bowl, cover with plastic wrap and let rise in a warm spot until doubled, approximately 30-45 minutes.
Place the risen dough on a floured flat surface (ex. kitchen counter) gently deflate and flatten into a rectangle. Cut the dough into 8 even pieces. Shape each piece into a thin oval (beaver tail shape). Use a sharp knife to carefully score the top of the beaver tails to create small square sections (to replicate a beaver tail).
Place the shaped beaver tails on a floured cookie sheet and cover with a lint free towel. Set aside to rise 10 minutes.
In a large skillet or deep pot, heat enough oil to come 2″ up the sides on medium-high heat.
Working in batches, fry the beaver tails 2-3 minutes per side or until golden brown. Remove from the oil, drain on a paper towel, set on a cooling rack to cool. Repeat with all beaver tails.