Preheat oven to 450°F. Prick potatoes several times along top with tines of a fork then roast 1 hour or so, until very tender.
When potatoes are just cool enough to handle, split them lengthwise and scoop out the flesh into a ricer or food mill, or push it through a fine strainer into a bowl (you will need to do this in batches). Warm EVOO in a small skillet or pot then melt butter into oil; add to potatoes. Season with salt, pepper and nutmeg then add cheese and 1 cup flour. Mix to combine. Using your hands, work in the egg yolks so they are evenly distributed throughout.
Dust a work surface with remaining 1/2 cup flour. Turn potato dough out onto the work surface and immediately knead it into a fat log. Cut into pieces then roll each piece into snakes about 3/4-inch wide. Cut snakes into 1-inch pieces then mark each piece with tines of a fork. Keep gnocchi covered with a kitchen towel and use in no more than 12 hours or freeze.
For Tomato Basil Sauce, heat a large sauté pan over medium heat with EVOO, 2 turns of the pan. Add butter and melt it into oil; add garlic and stir 1 minute. Add tomatoes, stock and basil, breaking up the tomatoes with a spoon. Add Parm rind and simmer sauce 20 minutes to break down tomatoes.
Cook gnocchi in salted water at rolling boil for about 2-3 minutes, until they float to the top of the pot. Remove with a spider and add them along with 1/2 cup of starchy liquid to the sauce. Toss gnocchi gently in sauce to coat and serve in shallow bowls topped with extra cheese.
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