Preheat oven to 350°. Butter an 8-inch round cake pan.
In a large bowl or the bowl of a stand mixer whisk together flour, sugar, baking powder, baking soda, and salt.
Add oil to the dry ingredient mixture. Beat together until no dry flour remains. Beat in eggs one at a time. Mix in vanilla. Scrape down the sides of the bowl. Mix in sourdough starter until incorporated.
Pour batter into prepared cake pan. Bake for 40-50 minutes until a toothpick inserted in the center comes out clean. Let sit for 10 minutes then remove from pan and cool on a wire rack.
When cake has completely cooled place on a large rimmed plate. Cut off the domed top with a serrated knife.
In a small mixing bowl or large spouted measuring cup whisk together whole milk, evaporated milk, and sweetened condensed milk. Slowly ladle or pour milk mixture over the top of the cake, allowing mixture to soak in before pouring more on. Cover and refrigerate at least 2 hours, or overnight.
Make frosting: Combine butter and powdered sugar in a large bowl or the bowl of a stand mixer. Mix until combined then scrape down the sides of the bowl. Beat together on medium-high speed until light and fluffy, about 4 minutes. Add vanilla, salt, and heavy cream and mix until incorporated.
Spread frosting onto the top of the cake. Sprinkle with cinnamon and serve.