Preheat the oven to 325°F.
Place the rolled oats in a bowl and add the Dr. Pepper. Let the oats soak for 10 minutes so that they’re rehydrated and soft.
Make the cake batter: in a stand mixer fitted with a paddle attachment, beat together the butter with the brown and granulated sugars. Mix until well incorporated, about 3 minutes. Add the eggs, working one at a time until each egg is mixed in. Add the vanilla extract and beat the batter on high for 5 minutes until the volume has doubled (this step will make for a nice, fluffy cake.) While the batter is mixing, sift together the flour, baking soda, spices, and salt. After the 5 minutes of mixing, slowly fold in the flour mixture, then add the Dr. Pepper–oatmeal mixture (the entire contents) and mix until just combined.
Split the batter evenly between two 9-inch round greased (or nonstick-sprayed) cake pans fitted with a piece of parchment paper on the bottom. Smooth out the top of both cakes. Place in the oven and bake for 50 to 60 minutes until golden brown and the top springs back slightly when pressed. Check the cakes with a toothpick or with a thermometer. The cake will be done when the toothpick is clean or the center of the cake is 210°F.
While the cake is baking, evenly spread out the coconut on a baking sheet. Place in the oven for 10 minutes or until the coconut is golden brown. Remove the coconut to a plate or bowl and set aside.
When the cake is done, transfer to a wire rack and let cool in the pan for 10 minutes. Turn out cakes onto a wire rack and let cool completely, about 30 minutes.