Preheat oven to 350ºF. Line an 8x8" baking pan with parchment paper.
Beat butter, sugar, and molasses in a stand mixer on high until light and fluffy, about 3 minutes. Beat in egg, scraping down sides of the bowl once with a rubber spatula.
In a separate bowl, whisk together flour, ginger, cinnamon and salt. Add to butter mixture with mixer speed on low and beat to incorporate.
Scrape batter into prepared pan, using lightly-dampened hands to press it evenly into the corners (it'll be stiff). Bake for about 20-22 minutes, until sides are pulling away from the pan and top just loses its sheen. Cool 5 minutes in pan, then transfer to a wire rack to cool completely.
To make icing, beat the butter, cream cheese, sugar and vanilla together in stand mixer with whisk attachment until light and fluffy, about 3 minutes. Spread over completely-cooled gingerbread bars.
Drain pomegranate seeds on paper towels, dabbing them gently to remove moisture from the surface. Scatter seeds over pomegranate seeds. Bars keep at room temperature for a day. If storing longer than that, hold off on the pomegranate seeds until just before serving.