2. Combine butter, water, sugar, salt and cayenne in a large saucepan. Cook until butter melts. Add 2 cups of flour all at once. Reduce heat and stir constantly with a wooden spoon until mixture is stiff and forms a ball-like mass, about 2 to 2 1/2 minutes. Pour into mixing bowl; using a mixer with a paddle attachment, beat 1 minute at medium-low speed to cool the mixture. Increase speed to medium; add eggs one at a time, beating to incorporate before adding the next. Batter should be firm, not runny. If necessary, blend in an additional ½ cup flour. Fold in cheese. Drop by tablespoons onto baking pan lined with parchment paper. Sprinkle with paprika.
3. Bake 10 minutes, turn the pan, and bake 10 more minutes. Leftover puffs can be frozen.