Thaw raspberries, if frozen. Place 1 cup berries in blender or food processor. Cover and blend or process until smooth. Press pureed berries through fine-mesh sieve into bowl. Discard seeds. Add liqueur and jam to pureed berries; whisk until smooth.
For frappe, in blender or processor combine berry mixture, gelato, and milk. Cover and blend or process just until combined, stopping blender to scrape down sides as needed. Stir in chopped chocolate or crushed cookies.
Divide remaining berries and frappe between two chilled glasses. Top with chocolate or cookies. Serve with long-handled spoons. Makes 2 servings.