In a large 3-quart saucepan, combine water, milk, butter, granulated sugar, and salt. Bring to a boil over medium heat, stirring frequently.

Remove from heat and stir in 1 cup flour all at once using a wooden spoon. Once incorporated, place the saucepan back over medium heat and stir constantly for another 1 1/2 to 2 minutes to release extra moisture and partially cook the flour. The dough will look smooth and a thin film will form on the bottom of the pan.

Transfer the dough to a large mixing bowl and use an electric mixer to beat on medium speed for 1 minute to cool the mixture slightly. Add 4 eggs, adding them 1 at a time and allowing eggs to fully incorporate between each addition. Once all eggs are incorporated, beat another minute until the dough is smooth and forms a thick ribbon when you pull up on the whisk.

Transfer dough to a piping bag with a 1/2-inch opening, or use a large zip bag and cut a 1/2-inch opening at the tip.

Heat oil to 375˚F in a dutch oven with a thermometer attached, or in a deep fryer. Once oil is hot, pipe 1-inch lengths into the hot oil, swiftly cutting the dough as you pipe into the oil. Pipe closer to the surface of the oil to avoid oil splashes.

Fry 4-5 minutes total, turning them over halfway if they don't turn on their own then transfer to a paper-towel-lined plate to soak up extra oil then dust with powdered sugar to serve.