In a large bowl, whisk together warm water, milk, and yeast.

Add sugar, flour, and salt. Mix using a stand mixer with a dough hook until combined, then knead for 1 minute until soft and elastic.

Transfer dough to a buttered bowl, cover with plastic wrap and a towel, and let rise in a warm place until doubled in size (about 1 hour).

Brown the butter in a pan over medium heat (5–6 minutes), then transfer to a bowl.

Stir in vanilla, maple syrup, and powdered sugar until smooth. Set aside.

Divide risen dough into 6–7 pieces and roll into balls. Flatten into thin ovals, oiling hands as needed.

Heat 1 inch of oil to 350°F in a frying pan.

Fry dough in batches until golden and bubbly on both sides. Drain on a wire rack.

Brush with maple glaze and optionally dust with powdered sugar. Serve warm.