In a medium saucepan, combine milk, water, butter, sugar, and salt. Bring to a boil over medium heat, stirring frequently.
Remove from heat and immediately stir in the flour with a wooden spoon until fully incorporated.
Return the pan to low heat and stir for about 2 minutes to partially cook the flour and remove excess moisture. You’re looking for a smooth dough ball with a thin film forming on the bottom of the pan.
Transfer the dough to a large mixing bowl. Using a paddle attachment, mix on medium speed to cool the paste. When the sides of the bowl feel warm, reduce to medium-low and add the eggs one at a time, scraping the bowl as needed. The dough is ready when fully incorporated, smooth, and forms a thick ribbon when lifted.
Heat 2’’ of vegetable or canola oil in a deep pan to 350–375°F.
Fit a pastry bag with a large open star tip (1M Wilton) and fill halfway with the dough. Pipe the dough a few inches above the hot oil and cut the ends with kitchen scissors. Avoid overcrowding the pan.
Fry the churros until golden brown and crispy on both sides, then transfer to a paper towel-lined plate.
Mix the cinnamon and sugar together until well combined and roll the churros in the cinnamon-sugar mixture while still warm.