Preheat oven to 350 degrees F.
Line a cookie sheet with foil. In a medium saucepan, combine sugar, butter, and corn syrup. Cook mixture over low heat until butter melts; remove from heat. Stir together flour and ginger; add dry mixture to butter mixture, mixing well. Stir in liqueur, if desired. Drop batter by rounded teaspoons 3 to 4 inches apart onto the prepared cookie sheet. Bake only 2 or 3 cookies at a time because you must work quickly to form the cones before they cool and become brittle*.
Bake in oven for 9 to 10 minutes, or until bubbly and golden brown. Quickly invert cookies onto another cookie sheet, and wrap each cookie around the greased handle of a wooden spoon or a metal cone. When cookie is set, slide cookie off spoon or cone; cool on a wire rack. Fill cookies with filling. To store: Place unfilled cookies in a single layer in an airtight container; cover. Store at room temperature in a cool, dry place for up to 3 days or freeze unfilled cookies for up to 3 months. Thaw cookies and fill.
*If cookie gets too brittle to roll, run back in the oven for 1 minute to soften.
Soften cream cheese in milk. Add sugar, 1 cup at a time, blending after each addition. Add melted chocolate and salt. Beat until smooth.