Preheat oven to 400F and line a baking sheet with parchment paper. In a saucepan over medium heat, bring water, butter, sugar, and salt to a rolling boil. Remove from heat and add gluten free flour all at once, stirring vigorously with a wooden spoon until the mixture forms a smooth ball that pulls away from the sides.
Let the dough cool for 3 minutes, then add eggs one at a time, beating vigorously after each until the dough is smooth, glossy, and thick enough to hold a shape.
Drop rounded tablespoons of dough onto the prepared baking sheet, about 2 inches apart, making about 12 puffs. Use a wet finger to smooth any peaks on top. Bake for 25 to 28 minutes until puffed, golden, and hollow-sounding when tapped. Do not open the oven during baking. Let cool completely.
Whip heavy cream, powdered sugar, and vanilla extract together until stiff peaks form. Slice each cooled puff in half horizontally and pipe or spoon a generous amount of whipped cream inside.
Melt chocolate with heavy cream in 20-second microwave intervals, stirring until smooth. Drizzle the chocolate ganache over the top of each cream puff. Let set for 10 minutes before serving.