For the cookies: Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
Whisk together the flour, graham cracker crumbs, baking powder, baking soda and salt in a medium bowl. Set aside.
Beat together the brown sugar, butter and vanilla in a large bowl with a stand mixer on medium-high speed until light and fluffy, about 2 minutes. Add the egg and beat until combined. Reduce the speed to low and add the dry ingredients in 3 batches, alternating with the milk, beginning and ending with the dry ingredients; beat after each addition until just combined.
Scoop tablespoon-mounds of batter and place on the prepared baking sheets about 1 inch apart. You should have 20 cookies per baking sheet.
Bake, rotating the baking sheets halfway through, until the tops of the cookies spring back when lightly touched, 10 to 12 minutes. Let cool on the baking sheets for 5 minutes, then transfer to wire racks to cool completely, about 30 minutes. Using a small fine-mesh sieve, dust the tops of the cookies with confectioners' sugar.
For the filling: While the cookies cool, whisk the cream cheese and marshmallow creme together in a medium bowl with a handheld mixer until smooth and well combined. Transfer to a piping bag fitted with a medium round tip.
Gently fold the strawberries and jam together with a rubber spatula in a medium bowl until combined; set aside.
Flip half of the cookies so they are flat-side up; pipe a ring of cream cheese filling around the edge of the cookies to create a “dam,” then spoon about 1 teaspoon of the strawberry filling in the center. Sandwich them with the remaining cookies flat-side down. Using a small fine-mesh sieve, dust the tops of the cookies with confectioners’ sugar.