Make the dough:

1. In a large mixing bowl, combine warm water and milk. Sprinkle yeast on top and whisk.
2. Add sugar, flour, and salt to the bowl.
3. Using a stand mixer with a hook attachment, mix until the dough forms, then knead for 1 minute until soft and elastic.
4. Transfer the dough to a buttered bowl, cover with plastic wrap and a towel, and let it rise in a warm place for about 1 hour until doubled in size.

Make the glaze:

1. Brown the butter in a pan over medium heat for 5 to 6 minutes until it bubbles and browns. Be careful not to burn it.
2. Transfer the browned butter to a bowl and add vanilla extract, maple syrup, and powdered sugar. Mix until smooth and set aside.

Frying and assembling:

1. Divide the risen dough into 6 to 7 equal balls and flatten each into a thin oval shape.
2. Heat vegetable oil in a frying pan to 350°F.
3. Fry the dough pieces until golden on both sides, then transfer to a wire rack to drain excess oil.
4. Brush the maple glaze on top of the fried dough and sprinkle with powdered sugar if desired.