Combine the water, soy milk, sugar, 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. If you are not using a non-stick pan, there will be a thin film on the surface of the pot.
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. We’re just trying to avoid mixing a ball of dough sitting in egg soup—that would be more difficult to mix! 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.
Next add in the shredded vegan cheese a bit at a time. I think we added it in thirds.
This is what our dough looked like.
Preheat the oven to 400° F.