How to Make It
Preheat the oven to 425°. Butter 2 large baking sheets.
In a food processor, puree the red bell pepper with the water and garlic until the mixture is as smooth as possible, about 2 minutes. Strain the pepper puree through a fine sieve set over a measuring cup, pressing hard on the solids with the back of a spoon to extract as much of the pepper juice as possible; you should have 1 cup. Stir in a little more water if necessary.
Transfer the red pepper juice to a medium saucepan. Add the butter, salt and pepper and cook over moderately high heat until the butter melts. Add the flour all at once and beat with a wooden spoon until the dough pulls away from the side of the pan and forms a smooth, shiny ball on the spoon. Scrape the dough into a bowl. Using an electric mixer at medium speed, beat in the eggs, 1 at a time, beating well between additions. Beat in the Pecorino Romano and cayenne.
Drop rounded teaspoons of the dough about 1 inch apart onto the prepared baking sheets. Bake the gouéres on the upper and middle racks of the oven for about 20 minutes, or until puffed and browned; shift the baking sheets from top to bottom and back to front halfway through baking. Serve the gougéres hot, warm or at room temperature.
If you use two different kinds of baking sheets when making this recipe, check that the gougères bake at the same rate. To help achieve even baking, consider investing in a pair of Silpats, reusable silicone pan liners. They are available in most kitchen stores, like Sur La Table.