In a saucepan, combine the water, milk, and unsalted butter. Heat over medium until the butter melts and the mixture comes to a gentle boil.
Remove the saucepan from heat and quickly stir in the flour, granulated sugar, and salt until the mixture forms a smooth dough.
Allow the dough to cool slightly, then add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract until fully incorporated.
Heat the vegetable or canola oil in a deep fryer or large pot to 350°F (175°C).
Transfer the dough to a piping bag fitted with a star tip. Pipe the dough into circular shapes directly into the hot oil.
Fry the crullers until they are golden brown on both sides, about 3-4 minutes per side. Remove them from the oil and drain on paper towels.
In a bowl, mix the powdered sugar with hot water or milk until smooth. Dip the warm crullers into the glaze to coat them evenly.
