In a medium bowl, combine the warm water, 3 tablespoons of granulated sugar, and the active dry yeast. Stir and let sit for 10 minutes until foamy.
In another bowl, whisk together the remaining 3 tablespoons of sugar, whole egg, yolk, warm milk, and vanilla extract.
In a large bowl, combine the all-purpose flour and salt.
Gradually add the egg mixture, yeast mixture, and melted butter into the dry ingredients, stirring until a dough forms.
Knead the dough on a lightly floured surface for about 5 minutes until smooth.
Place the dough in a lightly oiled bowl, cover with plastic wrap, and let rise in a warm spot for about 1.5 hours, or until doubled in size.
Roll the risen dough out on a floured surface to about 1/2-inch thickness. Cut into squares.
Heat vegetable oil to 360°F in a deep pot.
Fry squares in small batches for 1-2 minutes per side until golden and puffy. Drain on paper towels.
Dust liberally with powdered sugar and serve warm.