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To make the gingerbread bars: Preheat the oven to 350°F with a rack in the center. Line an 8" square pan with a parchment sling and lightly grease.
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In a medium bowl, whisk together the flour, gingerbread spice, baking powder, and salt.
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In a large saucepan or microwave-safe bowl, heat the butter over medium-low or microwave for 45 to 60 seconds, covered, on 50% power, until just melted.
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Whisk the molasses and brown sugar into the butter. Add the egg and vanilla and whisk until the mixture is shiny and emulsified.
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Add the dry ingredients to the wet ingredients and whisk until smooth. Transfer the batter to the prepared pan and spread it to reach the corners.
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Bake the gingerbread bars for 20 to 25 minutes, until set in the center.
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Remove the bars from the oven and let them cool slightly in the pan before using the parchment to transfer them to a wire rack. Let cool completely. (The bars can be made 2 days in advance; store airtight at room temperature.)
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To make the frosting: Working in a large bowl with a rubber spatula or handheld mixer or in the bowl of a stand mixer fitted with the flat beater, sift in the confectioners’ sugar and salt, then add the butter. Beat until a thick paste forms. Add the water and beat until the frosting is smooth and spreadable. Cover until ready to use.
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Once the bars are fully cooled, spread the frosting evenly over the top. (A small offset spatula is a helpful tool here.) Working quickly before the frosting sets, decorate with sprinkles and/or gingerbread spice. Slice into bars and serve at room temperature.
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Storage information: Store leftover frosted gingerbread bars well-wrapped at room temperature for up to 3 days.