Mix water, sugar, and yeast in a large bowl and let sit 5-10 minutes.
In a medium bowl, whisk the eggs, salt, vanilla extract and evaporated milk together.
Add egg mixture to yeast mixture and mix.
Stir in the melted butter, followed by the bread flour.
Using a spatula or your hand bring the dough together into a ball (I like to use my hand so you can feel whats going on). You will notice that this dough will be a little sticky, that's ok.
Coat a large bowl with oil, place dough in bowl and cover with plastic wrap.
Let rise at least 2 hours or place in refrigerator overnight.
Preheat oven to 350oF (180oC).
Roll dough to ¼-inch thickness and cut 1 1/2 inch squares. (This is easy to do with a pizza cutter.)
Place the squares on a baking sheet lined with parchment paper 1 inch apart and let the dough proof for about 45 minutes.
Brush each square lightly with milk and bake for 12-15 minutes, or until golden brown.
While the beignets are still warm, brush them with butter and generously dust with icing sugar.