Preheat oven to 400°F. Line two large baking sheets with parchment paper and brush the paper lightly with water. Whisk together tapioca flour, almond flour, and corn starch in a small bowl and set aside.

Combine butter, water, milk, sugar, and salt in a medium saucepan and bring to simmer over medium heat, whisking occasionally.

Once simmering, reduce heat to low and add flours, mixing well with a heat-proof rubber spatula. Cook, stirring and pressing the dough to combine for 3-4 minutes until it is very thick and a toothpick would stand upright in the dough. The dough will be very gummy almost like the texture of cooked mochi and a little oily. It's important to cook this long enough to thicken to cook off some of the moisture. The dough should also leave a thin film on the bottom of the pan. Transfer to a stand mixer fitted with a paddle attachment or medium bowl with a hand mixer and let sit to cool until it reaches 160°F. If some of the butter separates, this is okay!

In 4 additions, slowly add SOME of the whisked eggs, mixing well on medium-high speed between additions. You will need about 142g-150g of whisked egg, depending on how long you cooked the dough. At first, it will seem like it won't incorporate, but rest assured if you keep mixing it on medium-high speed, it will. When it's done, your dough should be shiny, thick, and smooth. When you pull your spatula or paddle from the bowl, the dough should stretch and form a V shape without being runny. When you drizzle some dough back onto itself, it should mostly hold its shape for 10-15 seconds.

Place a pastry bag (or large disposable plastic storage bag) fitted with a ⅜-inch round tip inside a glass and transfer the batter to the bag.

Pipe heaping tablespoon rounds onto the prepared parchment paper about 1.5 inches apart, using your finger to cut off the stream of batter between dollops. Use a wet finger to help form the edges of the dollops into perfect rounds if any have gotten lopsided. The gluten-free choux batter mounds will be much smoother and glossier than the non gluten-free ones - this is OKAY. They will puff up.

Unless your oven fits your baking sheets side by side, bake one sheet at a time on the middle rack for 20 minutes (See note below about cooking in an air fryer). Reduce to 350°F and bake for 6-10 additional minutes until the shell is browned and crisp and the inside is hollow and dry. Check if one is finished baking, pull one cream puff out of the oven, use a sharp knife to poke a thin hole in the top and let it cool for a couple of minutes. Slice it in half, if the dough inside seems very moist and eggy, continue baking it for another 3-5 minutes. Repeat. The inside should be mostly hallow, with some thin cooked dough around the edges. 

Remove from oven and use a sharp knife to poke a hole in the top of the cream puff shell to release the steam. Let cool for a few minutes on the pan before transferring to a wire rack to cool completely. Once cool, use a sharp or serrated knife to cut the cream puff shells in half lengthwise - they will be mostly hollow, with a film of cooked dough.

Meanwhile prepare the vanilla whipped cream. In the bowl of a stand mixer with the whisk attachment or a mixing bowl with a hand mixer, whisk the cream until it begins to thicken, but peaks have not formed yet. With the mixer running on medium low, add the sugar in a slow stream. Add the vanilla and continue whisking until pillowy soft peaks form. The cream should be thick enough to pipe, but not so thick that it looks lumpy (then it's over-whipped!).

Pipe or dollop cream onto the bottom half of each cream puff shell, then place the top back on. Use a fine mesh sieve to dust them with powdered sugar and serve the same day.