Combine dry ingredients: all-purpose flour, whole wheat flour, granulated sugar, kosher salt, and baking powder. Whisk together.
In a separate bowl, combine lukewarm water and active dry yeast. Let dissolve until cloudy.
Add milk and beaten eggs to the yeast mixture. Whisk together.
Make a well in the center of the dry ingredients and pour in the liquid mixture.
Gently incorporate everything with a spatula until no dry flour areas remain. The dough will be sticky.
Switch to kneading by hand for about 15 minutes, or until the dough is smoother, more elastic, and cohesive, though still sticky.
Cover the bowl and let the dough rise at room temperature for about an hour and a half, or until doubled in size and bubbly.
Chill the dough in the refrigerator for at least 4 hours, or preferably overnight.
Heat neutral oil in a Dutch oven or heavy-bottomed pot to 370-375°F (188-190°C).
Generously flour your work surface and hands. Pat the cold dough down into a rough rectangular shape.
Cut the dough into approximately 2.5-inch squares.
Gently separate the squares, ensuring they have space to prevent sticking.
Cover the cut beignets with a kitchen towel and let them rest while the oil heats up.
Carefully dust off excess flour from the beignets by shaking them or using a brush.
One by one, slip the beignets into the hot oil, being careful not to splash. Fry in batches, ensuring beignets have room to move.
Fry for about 2 minutes per side, or until golden brown and puffed up. Constantly monitor and regulate the oil temperature.
Remove the beignets from the oil using a spider or slotted spoon and place them on a wire rack set over paper towels to drain.
While still warm, generously dust the beignets with confectioners' sugar.
Serve immediately.
