Take your stand mixer and put in your warm water, yeast, and sugar. Let this bubble up to activate the yeast for about 5 minutes. While you're waiting, make your flax egg and set it aside. 

After your yeast has been proofed, then add your plant milk, soft vegan butter, salt, nutmeg, and flax egg; mix this together. Now add the flour and knead with the dough hook for about 5 minutes. Your dough shouldn't be sticky. If it's way too sticky, add 1 TB of flour until it's not, but be careful not to over flour. After 5 minutes, remove the dough with one hand, spray the bowl with cooking spray, and place the dough back in the bowl. 

Cover the bowl with a clean dish rag and put it in a warm place to rise. (I usually let my oven preheat to about 100 degrees, then shut the oven off and put my bowl in the warm but shut off oven to rise there. Rise for 1-1.5 hours.

While the dough rises, make the filling by combining all the ingredients. Take the butter and cut it in with a pastry cutter until combined. 

When the dough has risen, punch it down, roll it out in a rectangle (on a Silpat), sprinkle the filling onto half of the dough, and then fold the dough over it *Pictures posted above. You have two options... You can either braid it or roll it up, make a circle, pinch the dough together, and then make slits in it every couple of inches for a fun design. Or braid it; braiding is a little bit more challenging. Look at the photos above, where you cut the dough into three pieces and then try to pinch the dough together so that the filling doesn't fall out. Then combine the three pieces of dough at the start of your braid, then braid like you would a braid *as you can see, I'm not very good at this* But maybe you will be better. Make a big circle and pinch it together when the braid is done. Cover with a clean cloth and let rise in a warm spot for 45 minutes. 

Preheat to oven to 375 degrees. Bake this for 18-20 minutes. Check the dough in the middle to ensure it's not too doughy. Let this cool for a bit and make the frosting.

Make the frosting by combining the ingredients and stirring. If it's too thick, add a little more plant milk, a teaspoon at a time.

Frost your cake; I used a pastry brush, and if you are using sprinkles, then quickly sprinkle the three colors on, alternating the colors.