Preheat oven to 350F. Grease an 8x8" baking dish or cake pan. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine butter, molasses, and brown sugar. Beat together until smooth.
Add sour cream and egg, mixing to incorporate.
Add the flour, along with baking powder, baking soda, salt, cinnamon, allspice, and nutmeg. Mix on low speed just until incorporated. The batter will be thick.
Spread the batter into the prepared pan, then bake for 30-35 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Notes
The sour cream helps keep this cake nice and moist. If you don't have any on hand, you can substitute plain greek yogurt (preferably whole milk yogurt rather than nonfat).
I like to dust the top of the cake with a little powdered sugar, just for looks. Then we top the slices with whipped cream when served. You could also add a scoop of vanilla ice cream if preferred!