In a large bowl, mix together the flours and yeast.
Over medium-low heat, combine the water, salt, butter, and sugar until dissolved. Remove from heat and cool to lukewarm temperature (slightly warm to touch).
In a stand mixer with the dough hook (or hand knead), combine the flour and liquid mixture and egg for 7-10 minutes. As the dough comes together and lifts away from the bowl, use the window pane test to check for gluten developement.
Remove the dough from the bowl and place it in a lightly greased bowl. Cover and let it rise in a warm place for about 2 hours, or until double in size.
Pandan Filling: Meanwhile, as the dough is resting, make the two fillings. Using an immersion blender or food processor, blend the pandan leaves with water. Sieve it and discard the solids. Then combine the retained pandan water with 2 Tbsp coconut milk, 2 Tbsp sugar and 1 egg yolk. Set aside.
Cocoa Filling: Combine the rest of the ingredients together for the cocoa filling (1/4 c cocoa, 2 Tbsp softened butter, 1 egg white, 2 Tbsp sugar, 2 Tbsp coconut milk. Set aside.
Once the dough has doubled, punch it down and place it on a lightly floured surface. Roll out the dough to a rectangle 12" x 20". Spread the two fillings in an alternating pattern, either diagonal or length-wise stripes.
To shape, roll up the dough with the long side. Then, using a sharp knife, cut the dough down the middle the long ways in three sections (opposite you would a cinnamon roll) but leave about 1 inch attached. Braid by pulling the alternating outside strands to the middle. Try to keep the layers facing up. Tuck the end beneath itself for a prettier finish.
Brush the melted butter over the braid and sprinkle coarse sugar over the top.
Transfer the braid to a baking sheet (optionally lined with parchment or a silicone mat). Cover and let the braid rise and rest as the oven preheats to 350ºF. Bake for about 50 minutes, until golden brown and the bread feels firm to touch. Cool before slicing.
Notes
Window pane test: this is a common method to check that the dough has been kneaded enough. Take a small chunk of dough, about grape sized, and start pulling the edges. If the dough does not break, while allowing light to shine through (window pane), then it's good! If it breaks before the window pane effect, then knead and test again until you get there.
Double the filling if just using one of them.
For the coconut milk, use it at room temperature to make sure it combines well. If the braid is too long for your sheet pans, you can divide it in half and bake them as 2 separate loaves