Heat the oven to 400Â° F (204Â°C). Lightly coat 2 cookie sheets with butter.
In a medium saucepan, combine the water, butter, oil, salt, and cayenne pepper. Bring to a boil. Remove the pan from the heat and add the flour all at once. Stir the mixture with a wooden spoon until it forms a smooth paste.
With the wooden spoon, beat in the eggs one at a time, blending completely each time. Stir in the Cheddar cheese and minced chives or scallions.
Using a tablespoon, drop balls of batter onto the cookie sheets. Bake for 20 to 25 minutes or until the puffs are firm and well browned. Serve them warm or at room temperature.