Preheat the oven to 400°F (200°C). Line two baking sheets with parchment paper.
Sift the flour onto a piece of waxed or parchment paper. Add the thyme to the flour and mix it in with your fingers.
Combine the water and butter in a medium-size pan and bring to a boil over medium-high heat. Let the mixture boil for 30 seconds. Then remove it from the heat and add the flour and salt all at once. Beat the mixture vigorously with a wooden spoon. It will go together easily, creating a sort of thick paste. Continue beating until the mixture comes away from the side of the pan and forms a homogenous ball of dough, 20 to 30 seconds. The dough should not be sticky-it will be slippery from the melted butter-but it should hold together well and not stick to the pan or the wooden spoon. If it does, return it to the heat and continue beating until it dries out.
Remove the pan from the heat and let the dough cool slightly. Then add the eggs, one at a time, beating well after each addition. When they are incorporated, beat in the cheese.
Fill a pastry bag with a ½ inch (1.3 cm) round tip, then fill the bag with the dough. Place walnut-size portions of the dough on the baking sheets, leaving about 1 inch (2.5 cm) between them. Bake in the center of the oven until the gougères are puffed, golden, and crisp, 35 to 40 minutes.
Remove from the heat, remove from the parchment paper and let cool on a wire cooling rack. Makes 35 to 40 gougères.