Preheat oven to 175°C (350°F) and line baking sheets with parchment.
Cream 1 cup butter with brown sugar and granulated sugar until light and slightly fluffy.
Beat in eggs and 1 tsp vanilla until smooth.
Whisk flour, baking soda, baking powder, cinnamon, and salt in a separate bowl, then add to the wet ingredients and mix just until combined.
Stir in rolled oats by hand, then scoop tablespoon portions onto trays, leaving space to spread.
Bake 9 to 11 minutes until edges are set and centers look slightly underdone. Cool on trays 5 minutes, then move to racks.
Beat cream cheese and 1/2 cup butter until smooth, then add powdered sugar gradually and mix until fluffy. Add remaining vanilla and enough milk for a spreadable filling.
Pair similar sized cookies, spread or pipe filling on the bottom of one, then top with another cookie and press gently to sandwich.