Preheat the oven to 400 degrees F.
In a heavy-bottomed medium saucepan set over medium heat, combine water, butter (cut into small pieces), and salt. Stir constantly and be certain the mixture does not come to a boil. Once the butter melts, stir in the flour. Stir quickly until the mixture binds together. Continue to stir for another minute, while the pot sits on the heat.
Transfer the mixture to a bowl and let the mixture cool slightly, about 10 minutes. Stir in 2 eggs, one at a time. Be certain that the first egg is fully combined into the mixture before adding the second egg. Add the canned pumpkin and minced sage. Stir to combine.
Line a baking sheet with parchment paper. You can either spoon or pipe the dough onto the parchment paper. If you decide to pipe it, use a ½-inch plain tip or just use a coupler. Each gougère should be 1 to 2 inches in diameter, and they should be spaced 1 inch apart. Sprinkle a few grains of kosher salt on the top of each gougère.
Bake, without opening the door, for 10 minutes and then lower the temperature to 375 degrees F for another 15 minutes, or until the gougère are golden brown and crisp on the outside. Pierce each gougère with a small, sharp knife to release the steam, which will stop them from becoming soft. Serve immediately. If the gougère lose their crispness while sitting, reheat them in a 375 degree F oven for 3 minutes.