In a saucepan (before turning on the heat), combine milk, water, sugar, salt, and cornmeal. Whisk until smooth — no lumps!
Add butter, then turn the stove to medium heat. Stir continuously as the mixture thickens. After 3–4 minutes, it should start pulling away from the sides of the pot, that’s your sign it’s ready.
Remove from heat and stir in shredded cheese. Mix well so the cheese melts into the masa.
Let the dough cool until you can comfortably touch it. Wet your hands with water to prevent sticking. Roll tablespoon-sized portions into smooth balls, then shape them into small cylinders (about the size of a thick breadstick).
In a deep pan, heat 1½–2 inches of oil over medium-high heat. You’ll know it’s ready when a small piece of dough sizzles immediately.
Carefully add a few sorullos at a time. Fry for about 3–4 minutes or until golden brown. They’ll float to the top and release easily once done.
Place on a paper towel-lined plate to absorb excess oil. Serve warm — plain, with mayo-ketchup dip, or alongside a cup of coffee.