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Mix water, sugar, and yeast in a large bowl and let sit 5-10 minutes.
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In a medium bowl, whisk the eggs, salt, vanilla extract and evaporated milk together.
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Add egg mixture to yeast mixture and mix.
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Stir in the melted butter, followed by the bread flour.
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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.
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Coat a large bowl with oil, place dough in bowl and cover with plastic wrap.
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Let rise at least 2 hours or place in refrigerator overnight.
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Preheat oven to 350oF (180oC).
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Roll dough to ¼-inch thickness and cut 1 1/2 inch squares. (This is easy to do with a pizza cutter.)
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Place the squares on a baking sheet lined with parchment paper 1 inch apart and let the dough proof for about 45 minutes.
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Brush each square lightly with milk and bake for 12-15 minutes, or until golden brown.
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While the beignets are still warm, brush them with butter and generously dust with icing sugar.