Fill a large pot with water and add about a couple teaspoons of salt. Bring this to a boil over high heat.
Fill a large bowl with water and ice.
Lower the basil leaves into the boiling water for 15 seconds.
With a slotted spoon remove the leaves and put them immediately into the ice water to stop the cooking and to set the beautiful green color.
Remove the leaves from the ice water and lay on paper towels to drain. Set aside.
Bring the water back to a boil and add the potatoes.
Boil gently for 18 to 25 minutes until the potatoes are fork tender.
Drain the water off the potatoes, return to the burner and turn it down to low. Cover and let the potatoes steam for a moment to dry them a bit.
Put the cream and the Parmesan cheese together in a small saucepan. Heat over medium heat until the cream is simmering.
In a food processor with the steel blade, chop the basil leaves.
Pour the hot cream mixture through the feed tube and process until smooth.
Beat the hot potatoes with a handheld mixer until they lightly mashed.
Then slowly add the hot cream mixture and the salt and the pepper.
Continue beating until the potatoes are smooth and creamy.
Take a taste of this glorious concoction and add salt and pepper to your taste.
Serve hot with a sprig of fresh basil for garnish.