Step 1: Activate the Yeast

1. In a small bowl, combine warm milk, sugar, and yeast. Stir gently and let it sit for 5-10 minutes, until it becomes frothy. This means the yeast is active.

Step 2: Make the Dough

1. In a large mixing bowl, whisk together the egg, vanilla extract, and melted butter.
2. Add the yeast mixture and stir to combine.
3. Gradually add flour and salt, mixing with a wooden spoon or dough hook attachment until a soft dough forms.

Step 3: Knead and Rest the Dough

1. Transfer the dough to a lightly floured surface and knead for 5 minutes, until smooth and elastic.
2. Place the dough in a greased bowl, cover with a towel, and let it rest for 1 hour in a warm spot. It should double in size.

Step 4: Roll and Cut the Dough

1. Once risen, roll out the dough on a floured surface to ¼-inch thickness.
2. Cut into 2-inch squares or circles using a knife or cookie cutter.

Step 5: Fry the Beignets

1. Heat oil in a deep pan to 350°F (175°C).
2. Fry the beignets in batches, cooking each side for 1-2 minutes, until golden brown.
3. Remove with a slotted spoon and drain on a paper towel-lined plate.

Step 6: Dust and Serve

1. While still warm, dust the beignets generously with powdered sugar (and cinnamon, if using).
2. Serve immediately and enjoy with coffee, tea, or hot chocolate!