Combine cake flour, cocoa powder, baking powder, baking soda, and salt in a large bowl.
In a separate bowl, whisk together sugar, non-dairy milk, apple cider vinegar, non-dairy yogurt, oil, and vanilla bean paste.
Pour wet ingredients into dry ingredients and mix until just combined.
For the lava filling: Combine brown sugar, cane sugar, non-dairy butter, cocoa powder, flour, non-dairy cream, vanilla bean powder, and salt in a saucepan.
Cook over medium heat, stirring constantly, until thickened.
Stir in chopped chocolate and non-dairy milk until smooth.
For the raw brownie batter squares: Cream together brown sugar, cane sugar, and non-dairy butter.
Beat in cocoa powder, flour, non-dairy cream, vanilla bean paste, and salt until combined.
Fold in chopped chocolate.
For the chocolate buttercream: Cream together non-dairy butter and powdered sugar.
Beat in cocoa powder, salt, vanilla bean paste, and non-dairy cream until smooth and fluffy.
