Warm milk in a small bowl and sprinkle yeast and a pinch of sugar over the milk without stirring. Let is sit until it becomes foamy, about 3-5 minutes
In a separate small bowl, whisk egg, egg yolk, vanilla, and ¼ cup coconut sugar until smooth
Whisk in the yeast mixture until just combined
In a stand mixer with your paddle attachment combine flour and salt then add egg and yeast mixture and beat on low until just incorporated.
Switch to the dough hook, add all of your vegan butter and beat on medium-low speed until your butter is totally incorporated and the dough is a little sticky and smooth. This will be about 8-10 minutes.
Turn your dough out onto a floured surface, kneading it for 30 seconds until it is very smooth. It will be a little sticky, that is ok!
Transfer your babka dough into a greased bowl and cover with plastic wrap and let rise in a warm place until doubled in size, 1.5-2 hours (Read above for my best rising tips!)
Once doubled in size, let the dough chill in the fridge for 45 minutes, covered
While your babka is chilling, make your matcha filling by whisking together reserved egg white, coconut sugar, flour, and green tea matcha powder until clumpy
In a small pan on low heat, bring non dairy milk to a simmer
Once it is at a simmer, pour it over top of your egg white and matcha bowl with the vegan butter and whisk together until completely smooth and matcha has dissolved
Return the smooth matcha filling to the pan on low heat and whisk for 2-3 minutes until it gets just a bit thicker
Remove from heat and put in bowl until ready to spread on babka dough
Generously grease an 8X4 loaf pan
On a lightly floured surface, turn out chilled dough and roll into a 21x 12 rectangle and make sure the long side is facing you
use an offset spatula, spread your matcha filling all over the babka dough to the edges and sprinkle with 2 tablespoons coconut sugar
Roll up the dough, as your would cinnamon rolls, lightly pulling it towards you to maintain its thickness
Cut your dough log in half and set the halves touching, side by side
Place one half over the other, making an “X”, then twist the ends on both sides twice, making a total of 4 twists
Transfer twisted dough to your prepared pan, cover with a clean kitchen towel and let rise 30 minutes
During the final rise, preheat oven to 350F
Brush with egg and water mixture and sprinkle with turbinado sugar
Bake matcha babka, until golden brown about 45-50 minutes rotating the pan once halfway
remove from over and let cool in pan 10 minutes then turn out onto wire rack to cool completely before slicing (if you can wait!!)