For the pomodoro sauce: Bring a pot of water to a boil; prepare an ice water bath. In 2 batches, blanch the tomatoes in the boiling water for about 1 minute, then shock in the ice water. Remove and discard the skins. Seed the tomatoes. Strain the seeds from the liquid through a fine-mesh strainer; reserve the liquid and discard the seeds.
Put the peeled tomatoes, tomato liquid and a large pinch of salt in a large bowl. Mix the salt into the tomatoes and set aside.
Put the garlic in a saucepan and cover with the olive oil. Cook over very low heat until the garlic is golden and soft, about 15 minutes. Strain and reserve the oil.
Add the infused garlic oil and chile flakes to a large, heavy-bottomed stockpot. Turn the heat to low and slowly bloom the chile flakes, about 2 minutes. Add the salted tomatoes and liquid to the stockpot and increase the heat to medium high. Bring to a slight boil and skim any foam that rises to the top. Lower the heat to a simmer. Smash the tomatoes with a potato masher. Cook until reduced by one-fourth, 25 to 30 minutes. Adjust the seasoning with salt.
Remove from the heat and submerge the basil in the sauce to infuse it as it cools down. Set aside 2 cups of the sauce for the parmigiana; reserve the remaining 4 to 5 cups sauce for another use. It will keep in the refrigerator for up to 3 days and in the freezer for 3 months.
For the pumpkin parmigiana: Preheat the oven to 325 degrees F.
Peel the pumpkin, cut it in half and scoop out the seeds. Place it cut-side down on a cutting board and slice it crosswise into half-moons approximately 1/4 inch thick.
Coat the bottom of a glass or ceramic deep-dish pie plate with 1/2 cup pomodoro sauce and arrange one-third of the pumpkin pieces in a single layer on top of it. Drizzle with 2 tablespoons olive oil, sprinkle with 1/3 cup Parmesan and scatter one-third of the basil leaves over the top. Season with salt and pepper. Spoon 1/2 cup sauce to cover this layer, then repeat two more times, layering the pumpkin pieces, oil, Parmesan, basil, salt and pepper and sauce until just below the lip of the pie plate. Scatter the remaining 1/3 cup Parmesan on top.
Cover the dish with foil and bake until barely tender, about 30 minutes. Remove the foil and bake until browned on top and most of the liquid around the sides has evaporated, an additional 30 minutes. Let sit for 15 minutes before serving.