Preheat oven to 350º.
Cream butter and sugars. Add molasses, eggs, and vanilla, and mix well.
Add salt, soda, cinnamon, and ginger, and mix well.
Add oatmeal, and mix until combined. Add flour and mix until just incorporated.
Using a cookie disher if available, drop rounded tablespoonfuls of dough onto a parchment-lined baking sheet and bake for 10-14 minutes.
For filling, mix all ingredients in a bowl until smooth and fluffy.
Frost the flat side of half of the cooled cookies, and sandwich them together with an unfrosted cookie.
