Combine fresh cranberries, sugar, and water in a saucepan over medium heat. Bring to a gentle simmer, mashing cranberries slightly with the back of a spoon as they soften and release their juices, filling the air with a sweet-tart aroma. Continue simmering for about 10 minutes until the mixture thickens slightly and the cranberries burst.
Pour the hot cranberry mixture through a fine sieve into a jar or bowl, pressing gently to extract as much syrup as possible. Let the syrup cool to room temperature before refrigerating for at least 1 hour to chill and thicken further.
Once chilled, measure about 1 to 2 tablespoons of the cranberry syrup into each champagne flute. Gently pour the sparkling wine over the syrup, filling the glass about halfway.
Add a splash of orange liqueur to each glass, then top off with more sparkling wine, being careful to preserve the bubbles. Gently stir with a spoon or muddler to combine the flavors without losing fizz.
Garnish each mimosa with a few fresh cranberries and a sprig of mint for a festive, colorful finish. Serve immediately to enjoy the lively bubbles and vibrant flavor.