Make the pomegranate molasses: In a small saucepan, stir together the pomegranate juice, sugar, and lemon juice. Bring to a simmer over medium heat, then reduce the heat to low and cook for 20–30 minutes, stirring occasionally, until syrupy. Be careful not to burn the syrup. Remove the pot from the heat and let the pomegranate molasses cool completely before using. Any leftovers will keep in an airtight container in the refrigerator for up to 2 weeks.
Make the cocktail: Add a few tablespoons of sugar to a small plate. Dip the rim of a champagne glass in the pomegranate molasses, then in the sugar to coat.
Add ½ tablespoon of the pomegranate molasses to the bottom of the glass, then pour in the lemon juice and pomegranate juice. Fill the rest of the way with sparkling wine.
Float the pomegranate seeds on the top of the cocktail and garnish with the rosemary sprig.
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