1 stick plus 2 tablespoons unsalted butter, softened
3/4 cup sugar
1 large egg, at room temperature
1/4 cup unsulfured molasses
6 tablespoons unsalted butter, softened
2 cups confectioners' sugar
1 1/2 tablespoons fresh lemon juice
Preheat the oven to 350° and position racks in the upper and lower thirds. Line 2 baking sheets with parchment paper.
In a bowl, whisk the flour, baking soda, ginger, cinnamon and salt. In the bowl of a standing electric mixer fitted with the paddle, beat the butter and sugar at medium speed until fluffy, 3 minutes. Beat in the egg and molasses. Add the dry ingredients and beat at low speed until incorporated, scraping down the bowl.
Working in 2 batches, drop scant tablespoons of the dough onto the baking sheets, 3 inches apart. Bake the cookies for 20 minutes, until risen and fallen and slightly firm; shift the sheets from top to bottom and front to back halfway through for even baking. Let cool slightly, then transfer the parchment paper to racks and let the cookies cool completely. Bake the remaining cookies.
In the bowl of a standing electric mixer fitted with the paddle, beat the butter with the confectioners' sugar at medium speed until light and fluffy, about 3 minutes. Beat in the lemon juice.
Arrange the cookies in pairs on a large work surface. Spoon or pipe 1 rounded tablespoon of the lemon filling onto the flat side of half of the cookies. Sandwich with the remaining cookies, pressing them together so the filling spreads to the edge.
The sandwich cookies can be stored in an airtight container between sheets of wax paper for up to 1 week.