Place a rack in the center of the oven and preheat it to 350F. Lightly mist two 9-inch round cake pans with nonstick spray. Trace the bottom of one of the pans onto 2 pieces of parchment, then cut along the trace marks and line the bottom of each prepared pan.
To make the topping, mix the brown sugar and cinnamon in a small bowl and cut in the butter using a fork or two knives or a pastry blender until well combined and crumbly. Spoon half the topping into each of the prepared cake pans, spreading it evenly over the bottom of each.
To make the cake, place the cake mix, pudding mix and 1 tsp cinnamon in a large bowl and stir to combine. Add the milk, melted butter, eggs and 2 tsp vanilla and beat with an electric mixer on low speed just until incorporated. Scrape down the sides of the bowl and beat on medium speed for a minute or two, until the batter is smooth, scraping the sides of the bowl as needed. Divide the batter evenly between the two pans, spreading the batter over the topping and smoothing the tops with a rubber spatula.
Bake until the cakes are golden and the tops spring back when lightly touched – 18-22 minutes. Transfer to a wire rack to cool for 5 minutes, then run a thin knife around the edge of each cake and invert onto the wire rack to cool completely, topping side up, about 20 minutes longer.
To make the cream cheese frosting, place the cream cheese and butter into a medium bowl and beat with an electric mixer on low speed until combined, about 30 seconds. Stop the machine. Add the confectioners’ sugar a bit at a time, beating on low speed until the sugar is well incorporated. Add the vanilla and cinnamon and beat on medium speed until the frosting is fluffy, about 1 minute longer.
To assemble the cake, peel off the parchment paper and transfer one layer, topping side up, to a serving plate. Spread the top with about 1 cup of the frosting. Place the second cake layer, topping side up, on top of the first layer. Frost the side of the cakes. To make slicing easier, place the uncovered cake in the refrigerator until the frosting sets – about 10 minutes.