Combine the honey and water in a small saucepan over medium heat. Add the torn mint leaves and stir until the honey dissolves completely.
Reduce heat to medium-low and simmer for 5 minutes to let the mint infuse the syrup.
Remove from heat and strain the syrup through a fine-mesh sieve, discarding the mint leaves. Set aside to cool.
Peel the grapefruits and remove as much white pith as possible. Place in a blender and blend until completely smooth, about 1 minute.
Fill four champagne flutes about one-third full with the fresh grapefruit puree.
Drizzle a spoonful of the honey-mint syrup into each glass. Adjust to taste.
Top each glass with chilled prosecco and stir gently. Garnish with a fresh mint sprig and serve immediately.