Preheat oven to 350°F and line baking sheets with parchment paper.
Beat 1 cup butter with both sugars until fluffy, about 3 minutes. Mix in molasses, vanilla, and eggs until creamy.
Whisk together flour, cinnamon, baking soda, and salt. Add to wet ingredients in two batches, mixing on low until just incorporated.
Fold in quick oats by hand until evenly distributed.
Scoop rounded tablespoons of dough onto prepared sheets, spacing 2 inches apart.
Bake one sheet at a time for 9-11 minutes until tops look set but still soft.
Cool cookies on baking sheet for 10 minutes, then transfer to wire rack to cool completely.
For filling, beat 3/4 cup butter until fluffy. Add cream cheese in chunks and beat until smooth.
Gradually add powdered sugar starting with 1 1/2 cups, then increase to desired sweetness. Add vanilla and salt.
Beat in cream only if frosting is too thick.
Match cookies by size. Spread 1 1/2 tablespoons filling on bottom of one cookie, sandwich with another.
