Prepare and gather the ingredients for the choux pastry. Using the second listed amount of soy milk, mix it together with the Just Egg. Set aside for later.
Combine the water, soy milk, sugar, vanilla extract (if using), and butter in a small saucepan on medium heat. Mix it with a rubber spatula until the butter dissolves and then leave it for a few minutes until it starts to simmer.
Once the liquid ingredients begin to simmer, carefully add in all the flour. Turn the heat to low. Continue to mix until the flour is incorporated and no white flour spots remain. The mix will thicken into a dough and almost form a ball. It should come off the sides of the pan easily. This shouldn’t take more than about 3 minutes.
Scoop the dough out of the pan and into a mixing bowl or the bowl of a stand mixer. Avoid using a plastic bowl as the dough will be hot. Smash the dough down and flatten it to help release the heat. Leave it to cool for a few minutes. Alternatively, you can mix the dough over some ice or some ice packs to help it cool more quickly. You can also mix the dough for a few minutes in a stand mixer with a paddle attachment.
Once your dough is just barely warm or room temperature, add in the Just Egg mixture a few tablespoons at a time. The amount is up to you. It can just get messy with too much liquid. Mix it with the rubber spatula and allow it to fully incorporate in between each addition. The final consistency should just barely run off the spatula and look pipe-able. Add more soy milk a tablespoon at a time if your mixture is still too thick.
Preheat the oven to 410° F.
Line a half sheet tray AND a quarter sheet tray with parchment paper or a silicone baking mat.
Scoop the choux mixture into a piping bag with a small writing tip.
Make the swans' necks by piping in the shape of the number two (2) about 1.5-2 inches tall. Pipe at least 8 of them, but you can make extras.
Bake the necks in the oven for 8-10 minutes until lightly browned and slightly puffed. Then remove and allow to cool. But keep the oven on.
Remove the writing tip from the piping bag. With a 1/2 inch opening or smooth tip, use the remaining choux mixture to make the swan bodies. There should be enough dough for 7-8 swans.
Pipe small mounds of batter in the shape of a tear drop or pear, about 2-2.5 inches long and 1.5 inches at the widest point. Then pipe a smaller second layer on top. You can wet the tip of your finger and gently flatten the little tips that will form when you pipe the choux puffs.
Place the baking tray into the middle rack of the oven. Allow the puffs to bake until evenly golden brown. It could take from 40-45 minutes. Do not open the oven door while they are baking! This will lower the temperature of the oven and could interrupt the production of the steam inside the puffs that they need to expand. You can check on their color in the final few minutes of baking.
Once the puffs are golden brown, turn off the oven and leave the oven door open a crack for 10 minutes to allow the inside of the puffs to continue to dry out while also cooling down.