Make the Choux Pastry
Preheat oven to 400 degrees F and line 2 half sheet pans with parchment paper or silicone baking mats.
In a small bowl, mix together your gluten free flour and xanthan gum and set aside.
Add the salt, sugar, butter, and water to a medium saucepan. Heat over medium-high heat and bring to a boil.
Decrease the heat to low and add all of the flour into the hot liquid. Immediately stir it in the flour until it's moistened and has absorbed all the liquid. The dough will start to form into a ball. Continue to cook over low heat for about a minute.
Transfer the dough to the bowl of a stand mixer and let the dough cool, no more than 5 minutes. Then, use the paddle attachment to start beating the dough before adding the eggs. This will help re-incorporate the butter if it has separated a bit.
With the mixer running on medium-low speed, add the first egg. Once the egg is beaten and incorporated, add the second egg. Repeat this step until all the eggs have been mixed into the dough. The dough will look curdled at first but with the addition of each egg, the dough will smooth out and come together. Scrape down the bowl as needed during this process.
Once all the eggs are added, mix for 30 seconds to a minute. You want a smooth, glossy dough. Please note, gluten free choux pastry dough is much thicker than traditional dough made with all-purpose flour but should still be pipe-able.
Transfer the dough into a piping bag fitted with a large round tip. Pipe into rounds about 1 1/2 inches wide (about 1 heaping tablespoon of dough) or use a medium scoop to portion the dough. Space the rounds about 2 inches apart to allow for the pastry to puff while baking. Use kitchen shears to help snip the end of the pastry, if desired.
Once you've piped your rounds, dip your fingers in a small bowl of water then smooth out the top of the pastries. You want the surface of the dough as smooth as possible. This will prevent any points from burning and will help form a nicely shaped pastry.
Then sprinkle a very small amount of water over the pastry dough/baking sheet - you shouldn't be leaving large puddles of water, just enough to mist the baking sheet.
Bake the Choux Pastry for 25-30 minutes at 400 degrees. Then, remove from the oven and use a sharp knife to quickly poke a hole in the side of each pastry to help the steam release. Return the pastries to the oven, turn the oven off, and leave them in there for another 5 minutes. When done, the pastries should be dry in the center and hollow on the inside. You can leave them in the oven for an additional 30 minutes to an hour to completely dry them out, just make sure the oven is off.
Remove the baked pastries from the oven and cool completely on a wire rack before filling.
Make the Whipped Cream
Add the heavy whipping cream, vanilla extract, and powdered sugar to a large bowl.
Beat until medium peaks form (halfway between soft and stiff).
Serve immediately or refrigerate up to 2 hours before serving.
Assemble
Use a paring knife or a serrated knife to cut the top 1/3 off of each pastry shell.
Pipe the whipped cream into the pastry bottoms using a piping bag fitted with a round tip.
Place the tops back on each pastry and then dust the tops of the pastries with powdered sugar. Serve immediately. If serving later, place the cream puffs in the refrigerator after filling and then dust with powdered sugar just before serving.