Preheat the oven to 350°F (175°C) and grease a cake pan.
In a bowl, whisk together flour, cinnamon, nutmeg, salt, baking powder, and baking soda.
In another bowl, beat butter, brown sugar, and granulated sugar until creamy.
Add eggs, vanilla, and mashed sweet potatoes, mixing until smooth.
Gradually stir in milk and dry ingredients, alternating until combined.
Pour batter into the prepared pan and smooth the top.
Bake for 35 minutes, or until a toothpick comes out clean.
While the cake cools, whisk together powdered sugar, coffee, vanilla, and melted butter for the icing.
Drizzle the icing over the cooled cake, letting it drip down the sides.
Slice, eat, and wonder why you don’t make this more often.