In a medium pot, heat the butter, water, salt and sugar over a medium heat until the butter has melted and the water is boiling. Take off the heat and immediately dump in the flours then stir vigorously to get a thick paste. Keep stirring until the dough is smooth and comes away from the sides of the pot.
Let the mixture cool for a minute or two. Meanwhile crack the eggs into a small bowl or jug and beat together with a fork. Drizzle a bit of the beaten egg into the pot and beat it in until smooth. Repeat until you’ve mixed in all of the egg.
Scoop the mixture into a piping bag without a tip (or use a mechanical ice cream scoop or a tablespoon). Pipe or scoop the mixture onto the baking paper into ~3cm wide blobs (you should get about 10-12 of them), spacing them about 2-3cm apart. Use a wetted fingertip to smooth the tops of each blob.
Whack the choux into the hot oven then turn the heat down to 200oC (400oF). Leave to bake for 18-20 minutes – they should have puffed up but will still be soft. Turn the oven down to 180oC (350oF) and leave for another 10-20 minutes until the buns are slightly darkened on top and feel dry. As soon as you take them out the oven, cut each bun in half horizontally to let the steam out. Leave to cool on a wire rack.