In a medium saucepan, combine water, milk, butter, sugar, and salt. Heat over medium heat, stirring until butter is melted and mixture is simmering.

Add the flour all at once and stir vigorously with a wooden spoon until a smooth dough forms and pulls away from the sides of the pan.

Cook for 1-2 minutes, stirring constantly. This helps dry out the dough.

Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment. Let it cool for about 5 minutes, stirring occasionally.

With the mixer on low speed, add the eggs one at a time, making sure each egg is fully incorporated before adding the next. The dough should be smooth, thick, and glossy.

Fit a piping bag with a large star tip (about 1/2 inch). Fill the piping bag with the choux pastry dough.

Heat the vegetable oil in a large, heavy-bottomed pot or Dutch oven over medium heat to 350°F (175°C).

Carefully pipe rings of dough into the hot oil, about 3-4 inches in diameter. Cut the dough with kitchen shears or a knife as you pipe it.

Fry in batches, without crowding the pot, for 3-4 minutes per side, or until golden brown and puffed.

Using a slotted spoon, remove the crullers from the oil and place them on a wire rack set over a baking sheet to drain.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.

Dip the tops of the warm crullers into the glaze, letting any excess drip off. Place them back on the wire rack to set.

Serve immediately or store in an airtight container at room temperature for up to 2 days.