Preheat the oven to 350F and lightly grease a loaf pan or line with parchment paper and set aside.
In a large mixing bowl, whisk together the oat milk, apple cider vinegar, applesauce, brown sugar, white sugar, olive oil, and vanilla bean paste.
Next, add the dry ingredients to the bowl making sure to add the flour first followed by the baking powder, baking soda, salt, and cinnamon. Gently whisk the ingredients into the flour and then mix with the wet ingredients JUST until a thick batter forms and no large streaks of flour remain. It's important not to over-mix the batter or it will come out dense/dry. Keep in mind, some lumps in the batter are totally okay!
In a separate bowl, mix together the the cinnamon sugar filling ingredients (the sugar and cinnamon) and set aside.
Add ⅓ of the cinnamon cake batter to the greased loaf pan and use a spatula to spread evenly. Top with ⅓ of the cinnamon sugar filling and then use a butter knife to gently make a large swirl in the batter. Follow with another ⅓ of the batter and another ⅓ of the cinnamon sugar filling and repeat. Make sure not to over-swirl with the knife or you won't have thick layers throughout the bread. Finish with the remaining ⅓ of batter topped with the remaining ⅓ of the cinnamon sugar filling on top and swirl one last time with the knife.
Add the loaf bread to the oven and bake for 50-55 minutes until cooked through. Remove from the oven, run a butter knife along the edges to loosen any stuck pieces, and let cool for 10 minutes in the loaf pan. Then, remove the bread from the pan and let cool completely on a wire rack.
While the bread is cooling make the vanilla icing. Add the sifted powdered sugar, oat milk, and vanilla to a bowl and mix together until a thick glaze forms. Pour the icing over the cake, slice, and serve!