Prep the oven: Preheat to 350°F (175°C). Line two baking sheets with parchment paper.
Cream the butter and sugars: In a large bowl, beat butter, brown sugar, and granulated sugar until light and fluffy, about 2–3 minutes.
Add wet ingredients: Beat in eggs one at a time, then mix in vanilla and molasses until smooth.
Whisk dry ingredients: In a separate bowl, whisk flour, baking soda, baking powder, cinnamon, and salt.
Combine: Add dry ingredients to the wet mixture and mix just until combined.
Fold in rolled oats. Do not overmix.
Portion and bake: Scoop 1 1/2-tablespoon mounds (about a medium cookie scoop) onto baking sheets, leaving 2 inches between cookies. Gently flatten the tops with damp fingers for even baking.
Bake: Bake 9–11 minutes until edges are set and centers look slightly underdone.
The cookies will finish setting as they cool.
Cool: Let cookies rest on the sheet for 5 minutes, then transfer to a rack to cool completely.
Make the crème filling: Beat butter until creamy. Add marshmallow creme and beat until fluffy. Gradually mix in powdered sugar, vanilla, and salt.
Add milk 1 teaspoon at a time until smooth and spreadable.
Assemble: Pair cookies of similar size. Spread or pipe 1–2 tablespoons of filling onto the flat side of one cookie. Top with its match and gently press to distribute the filling.