Preheat oven to 350°. In a small bowl, whisk together flour, baking soda, cinnamon, and salt; set aside.

In a large bowl, with an electric mixer, beat sugar and butter until combined. Beat in egg, then molasses, until smooth. On low speed, gradually add flour mixture until a dough forms.

Drop rounded measuring teaspoonfuls of dough onto two ungreased (or parchment-lined) baking sheets.

Bake until centers are dry to the touch, 12 to 15 minutes; rotate pans from top to bottom and front to back halfway through. Cool 1 minute on baking sheets; then transfer to a rack to cool completely.

For the filling, whisk 12 tablespoons softened unsalted butter with 3 tablespoons light unsulfured molasses until smooth. Gradually whisk in 2 cups powdered sugar until smooth and spreadable.

To assemble, spread a rounded measuring teaspoonful of filling on the flat side of a cookie; place another cookie on top, and gently press. Repeat until all cookies are filled.