In a medium saucepan, combine cranberries, water, sugar, cinnamon sticks, cloves, and star anise. Bring to a boil over medium-high heat, then reduce to a simmer.

Cook the mixture for 10-12 minutes, stirring occasionally, until cranberries burst and liquid thickens slightly.

Remove from heat and stir in vanilla extract and ground nutmeg. Allow to cool to room temperature for at least 30 minutes.

Strain the mixture through a fine-mesh sieve, pressing solids to extract all liquid. Discard solids and refrigerate until ready to use.

Mix granulated sugar and ground cinnamon on a small plate. Run a lime wedge around glass rim, then dip into cinnamon sugar mixture to coat.

Fill prepared glass with ice cubes, about three-quarters full.

In a cocktail shaker filled with ice, combine spirit, 3 oz spiced cranberry mixture, and fresh lime juice. Shake vigorously for 15-20 seconds.

Strain cocktail into prepared glass over ice. Top with sparkling water or champagne, pouring gently.

Garnish with fresh cranberries, cinnamon stick, star anise, and optional rosemary sprig.

Serve immediately while cold and bubbly. Stir gently before sipping.