Pre-heat oven to 350; line baking sheets with parchment paper and set aside
Whisk flour, Oreo crumbs, baking soda and salt in a medium bowl and set aside
In the large bowl of an electric mixer, beat butter and sugars on high speed until light and fluffy
Beat in egg and vanilla on medium speed just until combined
Reduce mixer speed to low and slowly add dry ingredients but do not overmix; use a spatula to make sure all cookie batter is combined
Use a medium cookie dough scoop or tablespoon to make cookie dough balls on a baking sheet lined with parchment paper (about 1½ tablespoons each)
Bake cookies for 9-11 minutes or until edges have slightly darkened and centers appear set
Allow cookies to cool on a cooling rack; once cool, match each cookie with a second cookie of same size to make the cookie sandwiches and prepare buttercream
Beat butter and cream cheese in the bowl of an electric mixer with the paddle attachment on high speed for several minutes until butter is light and creamy
Add powdered sugar and vanilla and mix on low speed until combined then increase speed of mixer to medium-high and beat for several minutes until frosting is light and fluffy
Stir in Oreo crumbs until evenly distributed
Spread or pipe frosting onto bottom of half of the cookie sandwiches, about 1½ tablespoons each; lightly press remaining cookies down onto frosting to create sandwiches
Notes
Adapted from these graham cracker cookies Store cookies in an airtight container up to four days (eat within two for best texture). Can be frozen up to one month.
Recipe by Keep It Sweet Desserts at http://www.keepitsweetdesserts.com/oreo-overload-cookie-sandwiches/