Mix Dry Ingredients: In a large bowl, combine flour, yeast, sugar, and salt.
Add Liquids: Mix the warm non-dairy milk and water, then add to the dry ingredients. Mix until the dough comes together.
Knead the Dough: Turn the dough onto a floured surface and knead for about 5 minutes until smooth. You can also use a stand mixer with a dough hook.
Rest: Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for 1 hour or until doubled in size.
Incorporate Butter: Roll out the dough into a rectangle (about 12x18 inches). Evenly distribute the chilled vegan butter cubes over 2/3 of the dough. Fold the dough into thirds (like a letter), and then roll it out again into a rectangle. Repeat this folding and rolling process 3 times, chilling the dough for 15 minutes between each fold.
Chill: After the final fold, wrap the dough in plastic wrap and refrigerate for at least 1 hour or overnight.