Preheat oven to 350°F.
In a small bowl, combine the milk and apple cider vinegar and allow the mixture to sit at room temperature for 10 minutes.
Meanwhile in a large bowl, combine the flour, cinnamon, baking soda, baking powder, sea salt, brown sugar, and granulated sugar. Then, using a pastry blender or your hands, cut in ¾ cup plus 2 tablespoons of the vegan butter until a crumbly mixture is formed (reserve the last 2 tablespoon of butter for later). You want small pieces of oil to remain solid in this mixture (make sure to not overmix). Reserve 1 ¼ cups of this crumb mixture in a small bowl and set aside.
In another bowl, combine the coffee, vanilla extract, and yogurt. Then, add in the milk with apple cider vinegar and stir to combine. Pour the wet ingredients into the large bowl with the dry ingredients. Fold these together gently until combined (make sure not to overmix).
Pour the batter into a greased or non-stick 8 ½″ to 9″ springform pan. Melt the remaining 2 tablespoon of butter, then pour it into the reserved crumb mixture and use your fork to combine, creating an even more crumb-like topping. Sprinkle the crumb mixture over the cake.
Bake for 60-70 minutes until a toothpick comes out clean when inserted in the middle.
Allow the cake to rest for 10 minutes. Remove the outside of the spring form pan and allow the cake to cool for another 30 minutes before adding the icing on top.
To make the icing, just whisk together powdered sugar, vanilla extract, and nondairy milk. Drizzle it across the cake in whatever pattern you like. Store leftover cake in an airtight container for up to 3 days.