Begin by mixing warm water and whole milk in a bowl, then add the instant yeast. Allow the mixture to sit for about 5 minutes until frothy.

Next, add white sugar, salt, and all-purpose flour to the yeast mixture. Combine until a shaggy dough forms, then knead in the unsalted butter until smooth and elastic for about 5-7 minutes.

Transfer the dough to a greased bowl, cover it, and let it rise for about 1 hour, or until it doubles in size.

After the dough has risen, punch it down gently, turn it out onto a floured surface, and roll it out to about 1/2-inch thick. Cut into elongated shapes resembling beaver tails.

In a deep pan, heat vegetable oil to 350°F (175°C). Fry each dough piece for about 2-3 minutes per side until golden brown, flipping carefully.

While the Beaver Tails cool slightly, brown unsalted butter over medium heat. Stir until light brown, then add maple syrup, vanilla, and powdered sugar, whisking until smooth.

Drizzle the warm maple-brown butter glaze generously over each fried Maple Beaver Tail and let set for a minute before serving.