Preheat the oven to 425. Line two baking sheets with parchment or silicone liners.
Add the milk, butter, sugar, and salt to a medium saucepan. Bring the mixture to a simmer over medium heat, stirring frequently to prevent scorching.
Remove the milk mixture from the heat, and add the flour. Stir until the mixture is thick and there are no flour pockets remaining. Return the mixture to the heat and cook 2-3 minutes.
Move the hot dough mixture to a food processor or the bowl of a stand mixer. Mix for a minute or two to allow steam to escape. With the mixer running, add the eggs one at a time, mixing well after each addition, to form a shiny and smooth dough. Fold in the grated cheese by hand.
Using a medium cookie scoop or a tablespoon, scoop the dough into rounded mounds on the prepared baking sheets, spacing one inch apart. Place the pans in the oven, reduce the heat to 375, and bake 20-25 minutes, until golden brown. If you are baking pans on multiple shelves, rotate the pans halfway through baking to ensure even browning.