1. Preheat oven to 425ºF (220ºC). Line two baking sheets with parchment paper or silicone baking mats.
2. Heat the water, butter, salt, and cayenne in a medium saucepan over medium-high heat, stirring occasionally, until the butter is melted.
3. Dump in all the flour at once and stir the dough continuously until it forms a smooth ball, then keep stirring a another minute or two until it starts to leave a dry film on the bottom of the pan. (Drying out the dough will help the puffs rise.)
4. Remove from heat and, if using a stand mixer, transfer the dough to the bowl of the mixer, fitted with the paddle attachment. Let the mixer run at low speed for about a minute, to release the heat. If mixing the dough in the saucepan, let sit about two minutes, stirring it a couple of time to release the heat.
5. Add the eggs to the dough one at a time, beating vigorously on medium-high speed after each addition, making sure each egg is mixed in before adding the next one. The dough should be smooth and shiny. Stir in the 1 1/3 cups (110g) grated cheese, then crumble the blue cheese over the top and fold it into the dough. (Note: If you make pâte à choux frequently, you’ll notice the dough is softer than usual. There’s a photo at the top of the post showing how the dough should look.)
6. Using a spring-loaded ice cream scoop, a pastry bag fitted with a plain tip, or two soup spoons, form the dough into six 2 1/2-inch (6cm) mounds on each of the two baking sheets, evenly spaced apart. Sprinkle the mounds of dough with the remaining 1/2 cup of grated cheese.
7. Put the baking sheets in the oven. Bake for 10 minutes, then turn the heat down to 375ºF (190ºC), and bake until the gougères are well-browned, turning and rotating the baking sheets in the oven three-quarters of the way through baking. Baking time will be about 30 to 35 minutes, but ovens can vary so use the baking times as a guide. If they are getting too dark, remove them from the oven sooner. If they are still too light at the end of the estimated baking times, continue to bake them until they’re deep golden brown.