To make potato basil puree, boil a pot of salted water and fill a bowl with ice water. Add 2 cups of basil leaves to the boiling water for 15 seconds. Remove the basil, and plunge into the ice water. Drain, and set aside.
Add 2 pounds of peeled and quartered potatoes to the same pot of boiling water. Return to a boil, cooking for 25 minutes. Drain and return to the pot, evaporating remaining water. In a small saucepan over medium heat, bring 1 cup of half-and-half and 3/4 cup of Parmesan to a simmer.
Puree the basil in a food processor. Add the cream mixture and process until smooth. Next, beat the potatoes with a mixer. Slowly beat in the basil cream, 2 teaspoons of salt and 1 teaspoon of pepper.
To make maple sweet potato puree, preheat the oven to 375 degrees Fahrenheit. Place 4 peeled and chopped sweet potatoes in a mixing bowl. Add 1/4 cup of maple syrup, 2 tablespoons of olive oil, 2 teaspoons of salt and 1 teaspoon of pepper. Toss to coat and roast on a sheet tray for about 40 minutes.
In a saucepan over medium-high heat, melt 2 tablespoons of butter with 2 tablespoons of olive oil. Add 1 thinly sliced sweet onion, 2 tablespoons of maple syrup and salt and pepper to taste. Saut�� for two minutes and set aside. Add 1 tablespoon of hot water if the pan dries.
Process the sweet potatoes with 1 tablespoon of hot water. Add half the caramelized onions, and pulse a few times. Fold in the remaining onions, reserving some for a garnish.Learn more about Cooking