In a small pot over medium heat combine the milk, water, sugar, salt and butter. Bring to a rolling boil. Remove from heat. 

Add all the flour at once and vigorously stir until combined. Return to medium heat and cook, stirring vigorously for 2 more minutes or until the dough is shiny and smooth and a light film is sticking to the bottom of the pan. Remove from heat again. 

Transfer to the bowl of a stand mixer and refrigerate for 20 minutes or until the dough is slightly warm. 

Fit the mixer with the paddle attachment and add 2 eggs to the bowl of dough. Beat on medium speed until the eggs have fully incorporated. 

Add the third egg and beat to incorporate. Scrape the sides of the bowl, add the egg white and vanilla extract and beat on medium speed for 2 minutes or until fully incorporated. 

Cover the bowl with plastic wrap and refrigerate for 15 minutes. 

Lightly grease some parchment paper. Transfer the dough to a piping bag fitted with a large star tip. Pipe a circle of dough onto the greased parchment paper connecting the ends. 

Heat the vegetable oil in a deep pot. Once it reaches 360 degrees transfer the cruller to the hot oil with the help of a slotted spoon. Fry each cruller for 5 to 6 minutes or until golden brown. Remove from the oil and transfer to a plate lined with paper towels. Let the crullers cool down completely. 

In a small bowl combine all the glaze ingredients. Once the crullers have cooled off dip each one in the glaze. Set to dry in a rack.