1. Put milk, salt, vanilla, sugar, and butter into a small saucepan over a high flame. Bring to a rolling boil. Make sure all the butter is melted.
2. Once mixture is boiling, remove from fire and add flour all at once. Mix with a wooden spoon until mixture becomes a smooth dough that pulls away from the sides of the pot.
3. Transfer dough to a mixer with a flat beater. Mix two to three minutes, until partially cooled.
4. Add one egg and mix until incorporated into dough. Add another egg and continue mixing until incorporated. Before adding a third egg, check if dough is ready by taking a little between your fingers. If a “string” of dough forms, it’s ready and doesn’t need another egg. If not, gradually add half a beaten egg and continue mixing until incorporated. Then, test again.
5. When dough is ready, transfer to a pastry bag with a 2/3-inch (1-and-1/2-centimeter) serrated tip.
6. In the meantime, heat oil for deep frying in a pot, until it reaches 350 degrees Fahrenheit (180 degrees Celsius). If you don’t have a thermometer, insert a wooden spoon into oil. If small bubbles form around the spoon, oil is ready.
7. Gently pipe out strips of dough into hot oil and fry well on all sides.
8. Once churros are golden on all sides, use a slotted spoon to remove from oil and drain on absorbent paper.