Preheat oven to 350ºF (180ºC). Coat an 8-inch square cake pan with butter.
Add the oil, egg, sugar and molasses to a deep bowl; whisk until well-blended.
Add the flour,cocoa, baking powder, salt and spices to the bowl. Pour in 1 cup (240 ml) hot water (not boiling). Whisk until smooth and well-blended (batter will be very thin).
Pour the batter into the prepared pan. Bake until sides pull away from pan and a metal skewer inserted in the center comes out clean (a few dry crumbs are okay), 30 to 35 minutes. Let cake cool in pan on a wire rack.
Once cake is cooled, add softened mascarpone and butter to a medium bowl. Using a hand mixer, beat on high until light and fluffy, 2–3 minutes.
Add nutmeg, salt, vanilla, eggnog and confectioners’ sugar to bowl. Starting on slow, and slowly increasing speed to medium-high, beat frosting until light and fluffy, 3–5 minutes.
Spread frosting over cooled cake. Cut into squares to serve.