Preheat oven to 375 degrees Fahrenheit and place a piece of parchment paper into a round cast iron skillet with high sides or a cake pan.
Mix the almond milk and vinegar and let sit for 5 minutes to make "buttermilk".
In a large bowl, mix the whole wheat flour, all purpose flour, flax, nutritional yeast, sugar, baking soda, and salt to a large bowl. Mix together until combined.
Cut the vegan butter into the dry ingredients and rub your finger and thumb together to get small pieces of butter coated in the flour.
Add buttermilk and cheese and use your hands until they're well incorporated. This will be a very wet dough!
Sprinkle 1/4 cup whole wheat flour to your work surface and turn the dough out onto the surface. Sprinkle another 1-2 tablespoons of flour on top of the dough. Then fold the dough onto itself like a book and add another tablespoon or so of flour as you kneed. Kneed for another 5 minutes until it's no longer super sticky (it will still be a moist flour, but you want it to stop sticking to the surface with every turn.) Fold corners under to make a ball and set the ball in the cast iron. Cut a X on the top of the circle.
Bake for about 40-45 minutes, or until golden brown and a toothpick inserted into the middle comes out clean.
Remove from oven and place the loaf on a rack to cool. Slice and serve with vegan butter or vegan cream cheese.