Mix the water and active dry yeast together, then let it sit for 10 minutes.
Using a stand mixer with the whisk attachment, mix the sugar, salt, milk powder, unsalted butter, and vanilla extract on high speed until light and foamy. Then, add the eggs one at a time on medium speed, followed by the yeast mixture.
Change to the hook attachment and add the cake flour, bread flour, and baking powder. Beat on low speed, then increase to high speed until the dough pulls away from the sides of the bowl. Let the dough rise for one hour.
Transfer the dough to a lightly floured surface and roll it out to about 1/4 inch (5 mm) thickness. Cut the dough into 1-inch to 2-inch squares (2.5 cm to 5 cm). Heat 3 inches (7 cm) of oil in a frying pan over medium-low heat.
When the oil is fully heated, drop the dough in batches and fry until golden brown, turning the beignets frequently. Use a strainer to transfer them to paper towels to drain. Sprinkle generously with powdered sugar and serve warm.