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1
Set aside 1/4 cup of the heavy cream and a tablespoon of the butter. Add the remaining cream, basil, walnuts, olive oil, salt, butter, and garlic to the bowl of a food processor or blender and blitz for a few seconds. If you need to scrape the sides and blitz again. (You don't want big chunks of garlic in there.)
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2
Empty the contents of the processor into a bowl. By hand, mix in the grated cheeses. Set aside.
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3
Preheat your oven to 400. Boil the potatoes in salted water in an oven proof sauce pan until almost done, about 15 minutes depending on the size of the potatoes. Drain the water, and cut the potatoes in half, putting them back in the pan. Add the tablespoon of butter into the same saucepan and a few tablespoons of water. Cook on medium heat, moving around once in a while. After about 4 minutes, add the remaining 1/4 cup of heavy cream. Let the potatoes cook a bit longer without moving them too frequently, so they develop a golden crust. (Another 5 minutes or so.) The cream will start to look curdled, but don't worry.
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4
Add about 1/4 cup of the basil mixture to the pan, stir, and put it in the oven for another 10-15 minutes. (You may want to lightly tent your pan to avoid burning, but I didn't find it necessary.) Test by piercing with a sharp knife. The potatoes should be cooked through.
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5
When the potatoes come out of the oven, transfer to a serving bowl and pour another 1/4 cup of the pesto on top, mixing gently. You may have leftover pesto, but you'll be glad. (Green eggs for breakfast, anyone?) Serve hot.
