Cook sugar, brown sugar, and 1/4 cup strong brewed chicory coffee in a large saucepan over medium heat, stirring constantly, 4 minutes or until mixture reaches a syrup-like consistency. Stir in 1 3/4 cups strong brewed chicory coffee, half-and-half, and vanilla; bring to a simmer over medium heat, stirring occasionally. If desired, stir in 2 Tbsp. chocolate liqueur per 1 cup punch just before serving.