In a food processor, pulse together all dry ingredients to combine. Add the butter cubes and pulse until you have a coarse mealy mixture. In a large bowl, mix together molasses, whole milk, and vanilla. Stir in the dry ingredients until just combined. Divide into two parts, wrap in plastic wrap, and then refrigerate for an hour or overnight.
Preheat oven to 350° F. Roll out half of the dough on a floured surface until it's 1/4-inch thick. Cut out small shapes with a cookie cutter and place them 1 inch apart on a cookie sheet lined with parchment. Bake for 15 to 20 minutes, until crispy, and then repeat with the remaining half of the dough. (If you have the oven space, you can bake both halves at once.) It's important to make sure that the cookies are fully baked. If they're anything less than crispy, they have a weird texture that almost makes them taste like they are stale.
For the frosting:
Cream together butter and cream cheese. Add vanilla and salt. Gradually add the 1 1/4 cups of powdered sugar. Taste and add more sugar, if desired. Fold in sprinkles.