For the Charred Orange Sorbet, grate orange peel. Set aside. Remove white pith from orange. Cut orange crosswise into 6 slices. Place on foil-lined baking pan. Sprinkle with 2 tablespoons of the sugar. Broil 4 to 6 inches from heat 7 to 8 minutes or until lightly charred. Cool orange slices then coarsely chop.
Place remaining 2/3 cup sugar and reserved grated peel in blender container; cover. Blend on high speed until well mixed. Add orange juice, coconut milk and half-and-half. Blend until sugar is dissolved. Pour into medium bowl. Stir in chopped orange.
Refrigerate 2 hours or until well chilled. Pour into an ice cream maker. Freeze according to manufacturer's directions.
For the Spiced Cookie Bars, preheat oven to 375°F. Mix flour and allspice in medium bowl. Set aside. Beat butter and sugars in large bowl with electric mixer on medium speed until light and fluffy. Add egg, rum and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Spread in greased foil-lined 8-inch square baking pan.
Bake 20 to 25 minutes or until edges are golden brown. Cool in pan on wire rack. Cut into 4 squares then cut each square crosswise into 4 triangles.
For the Rum Sauce, melt 2 tablespoons of the butter in large nonstick skillet on medium-high heat. Place orange sections in skillet. Sprinkle sugar around oranges. Cook 10 minutes or until sugar begins to caramelize, gently stirring occasionally. Remove from heat. Add orange juice and rum. Cook 2 minutes, stirring occasionally. Remove from heat. Stir in remaining 1 tablespoon butter until melted. Serve Spiced Cookie Bar with a small scoop of Charred Orange Sorbet and drizzle with warm Rum Sauce.