Heat oven to 425 degrees. Line a baking sheet with parchment paper or a silicone baking mat.
Add the water, butter and salt to a medium saucepan. Let cook over medium heat until the butter is melted. After the butter melts, add the flour all at once and stir vigorously with a wooden spoon until combined. Continue cooking and stirring over medium heat for 5-7 minutes. The batter will look like play-dough, or thick mashed potatoes. Remove from heat and allow to rest for 5 minutes.
Beat 4 eggs in a small bowl. Using a hand mixer, beat 1/4 of the egg mixture into the dough. Repeat with the remaining eggs. Alternatively this can be done by hand with a wooden spoon, being sure to beat the egg in quickly so that it doesn't cook in the hot dough.
Stir in the chipotle peppers and cheese.
Beat the remaining egg with a tablespoon of water. Scoop small spoonfuls, about one and a half tablespoons, of the dough onto the prepared baking sheet. The dough can also be put into a piping bag and the gougeres piped out onto the baking sheet. These rise up, not out, so they only need a bit of space around them. Brush the dough with the beaten egg. Place in the oven and reduce oven temp to 375 degrees.
Cook for 20-25 minutes until the gougeres are golden brown. Rotate the pan halfway through the cooking time. They should sound hollow if tapped on the bottom. Remove from the oven and transfer to a cooling rack. Pierce a hole in the side of each gougere to allow steam to escape. Allowing the steam to escape will prevent them from collapsing.
For the Dip
Stir together all ingredients. Refrigerate until ready to serve.
These can be served hot or at room temperature.The calories shown are based on the recipe making 45 pieces, with 1 serving being 1 piece. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate.