In a large mixing bowl, combine the warm water, granulated sugar, and active dry yeast. Stir gently and let it sit for about 5-10 minutes until frothy.
Once the yeast mixture is frothy, add the slightly beaten egg, egg yolk, evaporated milk, and vanilla extract. Whisk together until fully combined.
In another bowl, whisk together the bread flour, salt, and any optional spices like cinnamon and nutmeg. Gradually incorporate the dry mixture into the wet ingredients, mixing until a dough begins to form.
Transfer the dough to a lightly floured surface. Knead the dough for about 5-7 minutes until it becomes smooth and elastic. If the dough is too sticky, add a little more flour as needed.
Place the kneaded dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm spot for about 1-2 hours or until it has doubled in size.
After the dough has risen, punch it down to release any air bubbles. On a floured surface, roll out the dough to about 1/4-inch thickness. Cut the dough into squares or rectangles.
In a deep skillet or pot, heat oil to 350°F (175°C). Use a thermometer to check the temperature.
Carefully drop a few pieces of dough into the hot oil, making sure not to overcrowd the pan. Fry for about 2-3 minutes on each side until golden brown. Use a slotted spoon to remove and transfer to a cooling rack lined with paper towels.
While the beignets are still warm, generously dust them with powdered sugar.
Serve your beignets warm alongside a cup of coffee or your favorite beverage.