Preheat the oven to 350℉ (180℃).
In a medium bowl, stir together the ingredients of the cinnamon swirl with a fork: dark brown sugar, cinnamon, and flour. Set aside.
In a separate large bowl, sift together the dry ingredients for the cake batter: flour, baking powder, baking soda and salt. Give the ingredients a whisk (about 10 seconds). Aside.
In a separate large bowl, beat together the butter, granulated sugar and brown sugar until fluffy. Be sure to turn off the mixer a few times and scrape down the bottom and sides of the bowl to ensure that there are no lumps. Then beat the oil and vanilla into the butter mixture.
With the mixer on a low speed, beat about ⅓ of the dry ingredients into the butter mixture. Then mix in the sour cream. Turn off the mixer and scrape down the bottom and sides of the pan. Mix in another ⅓ of the dry ingredients, turning off the mixer and scraping down the bowl afterwards. Then mix in the milk - I typically do this by hand with a wire whisk to avoid splashing. Lastly, mix in the last ⅓ of the dry ingredients. Be sure to stop mixing once everything is combined.
Grease the bundt pan with non-stick baking spray or pan release. Be sure to get into all of the crevices of the pan. Spoon about ⅓ of the cake batter into the pan and spread into an even layer. Then sprinkle about ½ of the cinnamon sugar filling on top. Spoon another ⅓ of the cake batter and spread into an even layer, then sprinkle the remaining ½ of the cinnamon sugar on top. Lastly, spoon the last ⅓ of the cake batter on top and smooth into an even layer.
Bake in the middle of the preheated oven for about 50-60 minutes. When finished, an inserted toothpick should come out clean or with some cinnamon sugar, but no gooey cake batter. You should see it starting to pull away from the sides of the pan and
Cool the cake in the pan for at least 25 minutes. When ready, very carefully invert the cake onto a cooling rack.