Preheat oven to 425 degrees F. Line two baking sheets with parchment.
In a large saucepan, heat the milk, butter, salt, pepper, mustard, and cayenne over medium heat until butter has melted.
IMix in the flour with a wooden spoon until it all comes together. Set aside dough to cool.
IPut dough into food processor; add the eggs, one at a time along with the grated comte cheese. Pulse in processor until everything is incorporated, but don't over do it.
ISpoon large teaspoons of dough on the baking sheets, brush with egg wash and sprinkle on remaining comte cheese.
IBake for 12 minutes until puffs are just about done. Remove from the oven and cool. Partially cut off tops of the puffs, so they almost have a lid.
ICut Ile de France Brie into small chunks, and place inside hole of each puff.
IBake an additional 3-5 minutes until cheese is melted.