Preheat the oven to 425° F.
Line 2 baking sheets with parchment paper or silicone baking mats.
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 to a food processor or stand mixer. If using a stand mixer, use the paddle attachment.
Mix for a minute to dissipate the heat.
Add the eggs one at a time with the processor or mixer 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. Be careful not to over mix.
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° F and bake for 20 to 25 minutes, or until the cheese puffs are golden brown.
Let cool slightly and serve. They won't last long!