01 - Combine warm milk, water, and yeast in a large bowl or stand mixer. Let stand for 5 minutes until mixture becomes foamy, indicating the yeast is active.
02 - Add sugar, melted butter, eggs, and salt to the yeast mixture. Mix on low speed until all ingredients are thoroughly combined.
03 - Gradually incorporate flour, mixing until a soft, sticky dough forms. Knead on medium speed for 5 to 7 minutes until dough is smooth, elastic, and pulls away from the bowl sides.
04 - Transfer dough to a lightly greased bowl, turning to coat all surfaces. Cover with plastic wrap or a damp towel and place in a warm, draft-free area. Let rise for 1 to 1.5 hours until doubled in volume.
05 - Punch down risen dough to release air. Turn onto a lightly floured surface and roll to 1/2-inch thickness. Use a sharp knife or dough cutter to cut rectangles measuring 4 by 1.5 inches.
06 - Arrange cut bars on parchment-lined baking sheets, leaving space between pieces. Cover loosely and let rise for 30 to 40 minutes until puffy and doubled in size.
07 - Pour 2 inches of vegetable oil into a heavy-bottomed pot or Dutch oven. Heat to 350°F, maintaining temperature throughout frying process for even cooking.
08 - Fry bars in batches of 3 to 4, cooking 1 to 2 minutes per side until deep golden brown. Use a slotted spoon to transfer to paper towels to drain excess oil.
09 - Whisk powdered sugar, maple syrup, milk, vanilla extract, and salt in a medium bowl until completely smooth and thickened. Adjust consistency with additional milk if necessary.
10 - While bars are still slightly warm, dip the top of each bar into the glaze, allowing excess to drip off. Place glazed bars on a wire rack set over parchment paper until glaze sets completely.