Preheat oven to 350°F (175°C). Grease a 9x13-inch pan with baking spray (can also be made in two 9-inch round cake pans).
Prepare the filling. Combine 1 cup brown sugar and 1½ Tbsp ground cinnamon in a medium bowl. Whisk well, then set aside.
Prepare the topping. Combine 2 Tbsp granulated sugar and 2 tsp ground cinnamon in a small bowl. Set aside.
Make the cake batter. Mix 10 Tbsp unsalted butter, 1¼ cups sugar, and ⅔ cup brown sugar in the bowl of a stand mixer fitted with paddle attachment for 2 minutes on medium speed, or until light and fluffy. Add eggs one at a time, mixing well after each addition.
Add the wet ingredients. To the mixer, add 1 cup sour cream, ¼ cup milk, and 2 tsp vanilla extract. Beat until smooth, about 1 minute.
Add the dry ingredients. In a small bowl, whisk together 2¾ cups cake flour, 2 tsp baking powder, ½ tsp baking soda, and 1 tsp Kosher salt. With the mixer on low, add the flour mixture to the batter, beating until just combined.
Prepare the coffee cake. Spread half the batter into the prepared pan, then sprinkle the filling on top. Spread remaining half of batter. Use a knife to swirl the filling into the batter.
Bake the cake. Use an offset spatula to even out the top of the cake, sprinkle the cinnamon sugar topping over the top, then bake for 55-60 minutes. (50-55 minutes for round cake pans). Allow to cool for 10-15 minutes before slicing and serving.