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1
Preheat oven to 400F. Bake potatoes until tender, about 1 hour.
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2
When potatoes have baked about 40 minutes, start making polenta. In small nonstick saucepan, bring 1 1/2 cups cold water and 1/2 teaspoon salt to a boil over medium heat. Gradually add cornmeal, stirring almost continuously with a wire whisk, When mixture starts to thicken, stir in 1 tablespoon oil with a wooden spoon.
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3
Reduce heat to low. Continue to stir until polenta is quite thick and creamy, taking care to scrape entire bottom and sides of pan, about 25 minutes. Remove from heat and cool slight[y, stirring occasionally to keep smooth.
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4
Remove baked potatoes from oven and cut in half lengthwise. When cool enough to handle, scrape flesh into large bowl (you should have 2 cups). Add Parmesan and butter; mash with a potato masher until evenly blended. Add egg, dried basil, remaining 1/2 teaspoon salt, pepper and cooled polenta, mash until blended. Sift flour over top and mix well with a fork. Cool 15 minutes.
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5
Line large baking sheet with sides with wax paper; flour lightly. With floured hands, spoon about 2 tablespoons potato mixture into your palm and gently roll into 1 3/4-inch ball. Flatten into 3/4-inch-thick disk and set aside on prepared baking sheet. Repeat with remaining potato mixture to make about 24 gnocchi.
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6
Bring large pot of lightly salted water to a gentle boil. Slide gnocchi in batches into water and simmer gently (surface should barely bubble) until they start floating to top, 5 to 6 minutes. With slotted spoon, remove cooked gnocchi to same baking sheet (dust off any excess flour first). Cool, then cover with plastic wrap and refrigerate at least 1 hour or up to 24 hours.
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7
In large skillet, heat a little oil over medium heat. Spread cornmeal in shallow dish and add a few gnocchi, turning to coat. Add gnocchi to skillet and cook until golden, 2 to 3 minutes per side. Transfer to serving platter.
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8
Repeat with remaining gnocchi, adding more oil to skillet as needed. Sprinkle with herbs and serve hot.
