Whisk together the potato protein powder, xanthan gum, and water until fully dissolved. Use an immersion blender to speed things up. Refrigerate for at least 15 minutes before using.
Pour the chilled potato protein mixture into the bowl of a stand mixer, add a pinch of xanthan gum, and whip until the meringue reaches soft peaks.
Add the sugar one spoonful at a time. Increase to full speed and whip until the meringue is glossy and holds stiff peaks, 6 to 10 minutes.
The vegan meringue should be firm, light, and silky. Use it immediately.
Baked meringue
Combine the powdered sugar and cornstarch, then sift them together. Gently fold them into the stiff meringue in 3 additions, being careful not to deflate it.
Pipe the meringue into your desired shape. Depending on the size, bake for 1 to 1.5 hours in an oven preheated to 105°C, or until completely dry.