In a large mixing bowl, combine warm water and warm whole milk. Sprinkle in instant yeast, followed by white sugar and salt. Gradually add all-purpose flour and melted unsalted butter, mixing until a soft dough forms.

Transfer the dough onto a floured surface and knead for about 5-7 minutes until smooth and elastic. Place in a greased bowl, cover with a warm kitchen towel, and let it rise for 1 hour or until it doubles in size.

Roll the risen dough out into a rectangle about ½ inch thick. Cut into beaver tail shapes. Heat vegetable oil to 350°F (175°C) and fry each piece for 2-3 minutes per side until golden brown.

Melt unsalted butter in a saucepan over medium heat until light brown. Remove from heat and whisk in vanilla extract, maple syrup, and powdered sugar until smooth.

Remove fried beaver tails from oil and drain on paper towels. Dip each pastry into the maple glaze while warm, then arrange on a serving platter.