In a medium saucepan, combine water, butter, sugar, and salt. Bring to a rapid boil, then stir in all the flour at once. Continue cooking over medium-high heat, stirring constantly, until the mixture pulls away from the sides of the pan and a thin film forms on the bottom.
Transfer the dough to the bowl of a stand mixer fitted with a paddle attachment. Mix for 1–2 minutes to release steam. Add eggs one at a time, mixing until each is fully incorporated. Finally, add the beaten egg whites and mix until the dough is smooth and glossy.
Heat canola oil in a deep saucepan to 370°F (if frying). Alternatively, preheat oven to 450°F (if baking). Prepare 12 parchment squares (3x3 inches) or line a baking sheet with parchment paper lightly greased with cooking spray.
Fill a piping bag fitted with a star tip with the dough. Pipe rings onto the prepared parchment squares or directly onto the baking sheet.
For frying: Place one or two crullers into the hot oil at a time, parchment side up. Remove the parchment with tongs as soon as it releases. Fry for about 2 minutes per side until golden brown. Transfer to a paper towel-lined plate to drain, then move to a wire rack to cool.
For baking: Bake at 450°F for 5 minutes, then reduce the oven temperature to 350°F and bake for an additional 15 minutes or until golden. Turn off oven, open the door slightly, and let the crullers sit for 5 minutes before removing.
Prepare the glaze by whisking together confectioners’ sugar, vanilla, and enough milk to achieve a pourable consistency.
Drizzle glaze over warm crullers or dip the tops for a more even coating. Allow glaze to set before serving.