For the chocolate cake: Preheat the oven to 350 degrees F. Butter and flour two 9-inch round cake pans.
Mix the flour, granulated sugar, cocoa, chipotle powder, baking powder, cinnamon, baking soda and salt together in a large bowl until blended. Add the oil, milk, vanilla and eggs and beat with an electric mixer until thoroughly blended, about 2 minutes.
Divide the batter evenly between the prepared cake pans and bake until a wooden pick inserted into the center of the cakes comes out clean, 20 to 22 minutes. Cool on a rack 10 minutes, then invert the pans to remove the cakes and cool completely.
For the cream cheese frosting: Beat the cream cheese and butter together in a large bowl with an electric mixer until thoroughly combined and smooth. Add the confectioners' sugar 1 cup at a time, beating well after each addition. Add the vanilla and continue to beat until the frosting is very smooth, about 2 minutes.
Spoon 2 cups of the frosting onto the top of one cake layer and smooth evenly with an offset spatula. Top with the second layer. Spoon just enough frosting on top to make a thin but even coating of frosting on top and all along the sides of the cake; it is okay if this frosting gets messy and full of crumbs. Freeze the cake until the frosting is firm, about 10 minutes.
Spoon the remaining frosting onto the cake and smooth evenly over the entire cake with the offset spatula. Dust lightly with cocoa powder and serve.