In a small bowl, combine powdered sugar and tapioca flour. Spray 8x8 pan with non-stick spray and coat with powdered sugar mixture completely. Tap the excess back into the bowl and set aside for coating the marshmallows later.
In the bowl of a stand mixer, combine pea protein, baking powder, and xanthan gum. Add cold water and mix with the whisk attachment for 10 minutes. The mixture will be thick with stiff peaks.
In a large heavy-bottomed pot, combine the sugar and agar powder. Add water, stir, and heat on high. Stir occasionally until mixture has reached 225-227°F.
As soon as the sugar mixture has come to temperature, carefully pour it quickly into the pea protein mixture while whisking at high speed. It is best to use a splatter shield if you have one or cover the mixture with a clean towel so you don't get splattered with the hot mixture.
Mix for 10 minutes on high speed. Scrape the bottom and sides with a rubber spatula halfway through. After 10 minutes, the mixture will be shiny, thick, and fluffy and should hold stiff peaks.
Quickly pour the mixture into prepared pan, using a rubber spatula to get it all out. Using a butter knife or offset spatula, quickly spread mixture to all edges and corners of the pan.
Cool in refrigerator for 1 hour to set.
Once completely set, turn the vegan marshmallow out onto a cutting board lightly coated in reserved powdered sugar mixture. Cut into squares however big you'd like and coat in reserved powdered sugar mixture. Enjoy immediately.