Preheat the oven to 425 degrees F. Line 2 baking sheets with parchment. Set aside.
In a saucepan, combine 1/2 cup water with the milk, butter, sugar and salt and stir over low heat until the sugar, butter and salt have melted. Raise the heat to medium and bring to a healthy simmer.
Take from the heat and immediately add the flour. Stir with a wooden spoon until the mixture thickens, is smooth and no flour lumps remain. Return to the heat and cook, stirring, until a film forms on the bottom of the pan. Continue stirring, careful not to scrape up the film, for a minute or two more.
Transfer the mixture (panade) to a food processor. Mix for a minute to dissipate the heat. Add the eggs one at a time with the processor running. Pay attention to the consistency of the paste. It should be smooth and shiny, so you may only need 3 of the eggs. Stir in the cheese.
Using a small cookie scoop, scoop generous mounds onto the parchment-lined baking sheets, spacing them an inch apart. Place in the oven, immediately reduce the heat to 375 degrees F and bake for 20 to 25 minutes, or until the cheese puffs are golden brown.
Alternatively, you could make the cheese puff dough ahead of time, scoop onto parchment-lined baking sheets and freeze until frozen solid. Then transfer to a ziptop bag and store in the freezer until you are ready to bake. Just increase the baking time by about 5 minutes.