To prepare compote, combine first 5 ingredients in a medium saucepan over medium-high heat. Bring to a boil, stirring until sugar dissolves. Stir in fruit. Reduce heat to medium; simmer 5 minutes or until fruit is tender and liquid is slightly thick. Pour into bowl; cover and chill at least 3 hours. Discard anise and cinnamon stick.
Preheat oven to 375°.
To prepare shortcakes, spoon pumpkin onto several layers of heavy-duty paper towels; spread to 1/2-inch thickness. Cover with additional paper towels; let stand 10 minutes. Scrape into a medium bowl using a rubber spatula. Add milk and 1/4 cup water, stirring to combine.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 5 ingredients (through nutmeg) in a large bowl, stirring with a whisk; cut in butter with a pastry blender or 2 knives until butter pieces are pea-sized. Add pumpkin mixture; stir just until moist. Drop dough by level 1/4 cup measures 2 inches apart onto a baking sheet coated with cooking spray. Flatten dough to 1/2-inch thickness using lightly floured hands. Sprinkle evenly with 1 teaspoon granulated sugar. Bake at 375° for 15 minutes or until golden. Remove from pan; cool on a wire rack.
Split shortcakes in half horizontally using a serrated knife. Spoon about 1/4 cup compote over bottom half of each shortcake; top each serving with 1 tablespoon crème fraîche and top of shortcake.
When mixing the dough for shortcakes, use a light hand and work quickly for the most tender cakes. If the recipe calls for kneading the dough, knead lightly only a few times so the dough doesn't become overworked.
Use a serrated knife to split the shortcakes. It will cut through the cakes without crumbling them.
You can bake the shortcakes up to a day ahead. Cool completely, and store at room temperature in a large zip-top plastic bag. To reheat, wrap in foil and heat at 350° for 10 minutes.
To freeze shortcakes, cool them completely, place in a heavy-duty zip-top plastic bag, and freeze up to two months. Thaw at room temperature, then reheat as instructed above.