Make a simple syrup by combining the honey and water in a small saucepan set over medium heat. Add the mint leaves and stir to combine. Simmer, stirring frequently, until the honey is completely dissolved.
Reduce heat to medium-low and simmer for another 5 minutes. Remove from heat and strain the syrup, discarding the mint leaves.
Place the peeled grapefruit in a high-speed blender and blend until completely liquefied, approximately 1 minute.
Fill four champagne flutes 1/3 full with the grapefruit puree and drizzle a spoonful of the honey-mint simple syrup into each glass. (Use more or less syrup according to taste). Stir briefly to combine, and then top off each glass with the chilled prosecco before serving. Cheers!