Line large rimmed baking sheet with parchment. Combine first 5 ingredients in heavy medium saucepan. Bring to boil over medium heat, stirring until butter is melted. Stir in flour and reduce heat to medium low. Stir vigorously until mixture forms large dough clumps and film forms on bottom of saucepan, about 1 minute. Remove from heat and cool 5 minutes.
Meanwhile, whisk eggs in medium bowl. Transfer 1 tablepoon beaten egg to small bowl and reserve. Add 1/3 of remaining beaten eggs to dough in saucepan and whisk until well incorporated. Add remaining eggs in 2 additions, stirring until eggs are completely absorbed after each addition (dough will be sticky). Mix in blue cheese. Drop dough by teaspoons onto baking sheet, forming about 24 walnut-size mounds and spacing about 1 inch apart. Using pastry brush, brush each mound with reserved egg, flattening any pointed tops.
Bake gougeres at 375 degrees until puffed, golden brown, and dry,30 to 35 minutes. Makes 24. (Bon Appetit)