Preheat the oven to 400 degrees . Prick the potatoes all over, then bake directly on the racks of the oven, rotating halfway through, until soft, about 1 hour 5 minutes. Let cool for 5 to 10 minutes.
Meanwhile, in a large pot or dutch oven, heat 2 tbsp. EVOO over medium-low heat. Add the onion and cook, stirring occasionally, until soft, 8 to 10 minutes. Stir in the garlic and crushed red pepper; cook for 1 minute. Add the tomatoes, season with salt and pepper and simmer, stirring occasionally, until thickened, about 15 minutes. Stir in the basil, then remove the pot from the heat and keep warm.
Halve the potatoes lengthwise and scoop out the flesh; reserve. Using a ricer or food mill, grind the potato flesh onto a baking sheet, then spread out evenly on the baking sheet and let cool completely.
Sprinkle the potatoes with the flour and toss lightly. Bring them into a pile and form a well in the middle. Beat the egg with 1 tsp. salt and pour into the well. Stir into the potatoes until a dough forms.
Knead the dough gently on a lightly floured surface. Slice into 4 equal pieces. Working with 1 piece at a time on a lightly floured surface,roll the dough into a 1/2- to 3/4-inch thick rope (about 16 inches long). Cut each rope crosswise into 1-inch pieces, sprinkle very lightly with a little more flour and transfer to a lightly floured or wax-paper-lined baking sheet.
In a large pot of boiling, salted water, cook the gnocchi in 2 batches until they float to the surface, 1 to 1 1/2 minutes, then simmer for another 10 seconds. Using a wire skimmer or slotted spoon, gently transfer the gnocchi to a bowl. Serve with the tomato sauce, drizzle with the remaining 1 tbsp. EVOO and top with grated parmesan.