In a large mixing bowl, combine the warm water, granulated sugar, and active dry yeast, stir to dissolve, and let sit for 10 minutes until foamy.

Whisk in the beaten eggs, evaporated milk, vanilla bean paste, and salt until smooth.

Add the flour in 2 to 3 additions, stirring until no dry flour remains and a soft dough forms.

Pour in the melted butter and mix until the dough is smooth, slightly tacky, and pulls away from the sides of the bowl.

Cover the bowl with a clean kitchen towel and let the dough rise in a warm place for 2 hours, or until doubled in size.

Lightly flour a work surface, turn the dough out, and gently press it into a rectangle, then roll it to 1/4 inch thickness.

Use a sharp knife or pizza cutter to cut the dough into 2 inch squares and place them on a parchment lined baking sheet.

Let the cut dough rest at room temperature for 15 minutes while you heat the oil.

In a deep fryer or large heavy bottomed pot, heat vegetable oil to 350°F, checking with a thermometer.

Fry a few beignets at a time for about 1 minute per side, or until puffed and deep golden brown, adjusting heat to maintain 350°F.

Transfer fried beignets to a wire rack set over a baking sheet to drain briefly.

While still warm, generously dust the beignets with powdered sugar and serve immediately.