Bring water, butter and salt to a rolling boil in a medium-sized saucepan.
When butter has melted, add flour, all at once, and whisk vigorously over medium heat until mixture forms a smooth thick dough that pulls away from sides of the pan.
Transfer dough to the mixing bowl of a heavy-duty electric mixer.
Using the paddle attachment, beat mixture on medium until slightly cool.
Add basil and mix until incorporated and dough is bright green.
Add eggs, one at a time, to mixture and beat until smooth.
Continue to mix for one minute.
Add cheese and proces until incorporated.
Line two cookie sheets with parchment paper.
Drop dough in tablespoon sized balls on cookie sheets, allowing about 1 inch of space between each.
Bake for 25 to 30 minutes or until lightly browned and crisp.
Serve while still warm.
(Dough may be piped onto cookie sheet using a piping bag and plain tip,#8 or#9.) Plan ahead: To prepare now and bake later, unbaked puffs can be refrigerated for up to six hours before baking, or frozen on cookie sheets, transfered to freezer bags or containers and baked directly from freezer.
Allow an extra five minutes baking time for frozen puffs.
Offer a spread: Make a delicious butter spread, such as sun-dried tomato butter, to complement the puffs.
Combine 1 pound of butter, 1 cup of sun-dried tomatoes, 1/2 cup of pine nuts and 1 tablespoon of fresh garlic in a mixing bowl.