In a large bowl or stand mixer, combine lukewarm water and yeast. Let the mixture do its job for about 5 minutes or until it's dissolved and looks a little frothy.
Lightly whisk evaporated milk, sugar, salt, egg, and vanilla extract. Add it to the yeast mixture.
Mix in about 2 cups flour and continue mixing with a hand or dough mixer. If using a stand mixer, mix for 1-2 minutes.
Finally, add melted butter and mix until the dough is sticky but smooth. Add additional flour as needed to make a soft dough.
Turn the dough onto a lightly floured surface and knead for 1-2 minutes. Place the beignet dough in a greased bowl, turning once to coat it. Cover loosely with a clean cloth and let rise in a warm, draft-free place for about 2 hours or until doubled in size.
Punch the dough down and remove it from the bowl. Roll out the dough on a lightly floured surface until ¼-⅓ inch thick.
Cut the dough into 1½-2-inch squares using a sharp knife or pizza cutter. Let it rest for about 10 minutes before frying.
Working in batches so as not to crowd the oil, fry the dough squares until puffy and golden brown.
Remove them from the oil, making a pit stop on a paper towel to soak up any extra oil.
Dust with powdered sugar immediately. Serve hot with café au lait, and enjoy!!!