Measure ¼ cup prosecco in a measuring cup and gently whisk in the packet of gelatin. The mixture will begin to foam. Let stand for 3 minutes.
In a medium saucepan over medium-high heat, combine the heavy cream, sugar, and salt. Cook the mixture gently until steaming but not boiling.
Whisk in the gelatin and stir until it's melted. Add one drop of red food coloring and stir to combine.
Remove from the heat and pour in the remaining ½ cup of Prosecco,and gently stir.
Let cool on the stovetop until you can safely touch the side of the saucepan, about 30 to 40 minutes.
Equally divide the panna cotta mixture among serving glasses or dessert cup dishes. Chill at least 3 hours, until set. This can be made 24 hours in advance.
To Serve: Remove panna cotta from the refrigerator. Serve with a fresh berry sauce by carefully spooning it onto the top of the panna cotta. Serve with fresh berries on the side.