Lightly grease a 9-inch round cake pan with earth balance.
Mix flour, baking soda, baking powder, salt, and coconut sugar together in a large mixing bowl.
Mix vanilla, oat milk, ACV, and melted earth balance together in a separate medium mixing bowl.
Combine wet with dry ingredients in a large bowl. Mix until just combined.
Transfer dough onto a heavily floured countertop, making sure you have a lot of rolling space.
Roll out into a long rectangle. The dough should be roughly 1/4 inch thick.
Combine lemon zest, strawberries, and all but one tablespoon of the lemon juice in a small mixing bowl. Smash together using a fork or pestle and mortar until a pulp-like consistency is formed. Strain out any excess liquid through a double-walled strainer.
Transfer back into a small bowl, add brown sugar, and mix together.
Spoon filling on top of the long rectangular dough sheet, leaving the edges empty for rolling.
Roll dough, starting from the long width of the rectangle until a long tube is formed.
Using your sharpest knife, cut 1-inch thick rounds from the tube and arrange them in a spiral starting from the outside of your cake pan.
Place in preheated oven and bake for 20 minutes.
While the buns are baking, combine cream cheese, earth balance, lemon juice, and vanilla in a small mixing bowl.
Slowly sift powdered sugar over top while mixing. Mix in oat milk in 2 tbsp increments until reaching desired consistency. A thicker glaze will be spreadable; a thinner glaze produces a drizzle.
Remove the buns from the oven and spread or drizzle the icing over top.