Preheat oven to 350F and spray a 12-cup bundt pan with nonstick baking spray. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl with an electric hand mixer), combine cake mix, oil, apple butter, eggs, and cinnamon. Mix on low speed for about 30 seconds to incorporate. Scrape down the sides of the bowl, then increase speed to medium-high for about 2 minutes.
Pour batter into prepared pan. Bake in preheated oven for about 30-33 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Let the cake cool in the pan for about 10 minutes, then run a knife along the edges of the cake to ensure it's loosened from the pan. Carefully invert the cake onto a serving plate to cool completely.
Once the cake is completely cooled, begin to prepare the icing by combining butter and brown sugar in a small saucepan over medium heat. Stirring frequently, bring it to a low boil and cook until the butter is melted and the sugar is dissolved (this will likely only take a couple of minutes, since it's a small amount).
Remove pan from heat. Carefully stir in 2 tablespoons of milk, mixing to incorporate.
Using an electric mixer, beat powdered sugar into the mixture until it's nice and smooth. If it seems thick, add another tablespoon of milk and mix to combine. You want it to be thin enough to spoon it over the cake, but not so thin that it just runs right off the cake.
Working quickly while the icing is still warm, spoon it over the cooled cake. Let the icing cool and harden for about 15 minutes, then slice and serve.