Caramelize the white chocolate: Add the white chocolate to a medium heatproof bowl and microwave in 45-second intervals, stirring between, until golden brown in color and completely melted and smooth.
Pour half of the melted chocolate onto a parchment paper-lined baking sheet and spread into an even layer. Freeze for 30 minutes, or until solid. Reserve the remaining melted chocolate.
Preheat the oven to 350˚F (180˚C). Line baking sheets with parchment paper.
Make the cookie dough: In a medium bowl, combine the butter, granulated sugar, brown sugar, and vanilla extract in a bowl and beat with an electric hand mixer until fluffy.
Add the egg and continue beating until fully incorporated.
Add the reserved melted white chocolate and beat to combine.
Sift in the flour, baking soda, salt, and espresso powder,l and fold into dough until no dry spots remain.
Chop the frozen white chocolate into chip-size pieces. Fold into the cookie dough.
Scoop the dough onto the prepared baking sheets, 6 cookies per pan, and bake for 12 minutes, until golden.
Make the filling: In a large bowl, combine the butter, powdered sugar, espresso powder, cinnamon, allspice, nutmeg, heavy cream, vanilla, and marshmallow fluff, and beat with a hand mixer until well combined and fluffy.
To assemble the pies, spread 2-3 tablespoons of filling on the flat sides of half of the cookies. Sandwich with the remaining cookies.