For the dough: In the bowl of a stand mixer, beat the butter, cream cheese, sugar, extracts, and salt together until light and fluffy, about 3 to 6 minutes on medium speed.
Reduce the speed of the mixer on low and slowly add the flour. Mix until just combined.
Divide the dough into two equal pieces.
Wrap each piece in plastic wrap and refrigerate until firm (about an hour).
Preheat the oven to 375 degrees F.
For the filling: Mix the white chocolate and crushed candy canes in a small bowl.
To assemble the cookies: Working with one piece of dough at a time, roll each piece of dough on a lightly floured surface into an 11-inch circle about 1/4 inch thick.
Sprinkle half of the filling over the dough.
Using a knife or a pizza cutter, cut each dough into 16 wedges (like you would cut a pizza).
Starting at the wide end, roll up each wedge into a cookie.
Lay the cookies on a parchment lined baking sheet.
Brush the cookies with the melted butter, and sprinkle with sugar.
Bake the cookies until they are a pale gold, about 20 minutes.
Immediately transfer the hot cookies to a cooling rack, and allow them to cool completely.
Repeat the same process with the second half of the dough.
Yields 32 cookies