Preheat the oven to 450°F, and line a baking sheet pan with a silicone mat (parchment paper can burn at this high of temperature!).
In a 2-quart saucepan with a heavy bottom (enamel-coated cast iron is best), add the butter, warm water, salt, and mustard powder (if using). Turn the heat to medium-high and melt the butter into the water.
When the butter and water mixture is at a rolling boil, dump in all of the flour at once.
Stir the mixture immediately, and then lower the heat to medium-low.
Continue to cook and stir the mixture for about 4 minutes, or until the dough is stiff, appears dry, and is clumping together in a ball around the spoon.
Move the dough mixture to a mixing bowl, and beat with an electric mixer for 1-2 minutes, until it is no longer hot to the touch.
While continuously beating, add 1 egg. Once the egg is fully incorporated, add the other egg while still beating.
Once the mixture is homogenous, it will be a soft, scoop-able dough.
Finally, beat in the grated cheese and chopped chives.
Using a cookie scoop that holds about 1 tablespoon of batter, scoop out 1 dozen balls and space them evenly on the baking sheet.
Bake for 5 minutes at 450°F, and then lower the heat to 350°F, and continue baking for another 20-25 minutes, until the puffs are golden brown.