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.
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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.
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