For the ravioli: Put the flour in a mound on a clean work surface and sprinkle with 1 teaspoon salt. Use your fingers to make a well in the middle of the mound. Crack 2 of the eggs into the well. Add 2 of the egg yolks to the well, followed by the heavy cream. Use your fingers to break up the eggs and yolks and combine with the cream. Work the flour into the egg mixture by gradually incorporating the flour from the inside of the well. When the flour is completely incorporated, knead the dough vigorously for 8 minutes until smooth and elastic. If the dough is too sticky to knead, dust with 1 tablespoon of flour at a time until you are able to knead it. Divide the dough into 4 equal pieces, wrap in plastic and set aside at room temperature for 30 minutes.
Mix the ricotta, Parmesan, remaining egg yolk, 1/2 teaspoon salt and a few grinds of pepper in a bowl until combined. Cover and refrigerate.
For the marinara sauce: Heat the oil in a medium saucepan over medium heat. Add the onion and cook, stirring occasionally, until softened, 8 to 10 minutes. Add the garlic and cook, stirring occasionally, until softened, 3 to 4 minutes. Add the tomatoes, oregano, sugar and crushed red pepper and stir to combine. Season liberally with salt and pepper. Bring to a boil over medium-high heat then reduce to a simmer. Simmer, covered, for 30 minutes. Discard the oregano and season with salt and pepper if needed. Cover and reserve.
To make the ravioli: Bring a large pot of salted water to a boil. Beat the remaining egg with 1 tablespoon of water and set aside. Lightly oil a baking sheet and set aside. Roll one of the pieces of dough into a 6-by-18-inch rectangle on a lightly-floured work surface (the dough should be very thin). Cut the sheet of dough in half lengthwise to create two 3-by-18-inch sheets.
Brush the entire surface of one of the pasta sheets with the egg wash. Working down the center, spoon 1 heaping teaspoon of the ricotta filling into 8 evenly spaced mounds. Gently lay the second pasta sheet over the first, matching up the sides. Gently press between the mounds of cheese to define 8 separate ravioli. Carefully push out air bubbles around the mounds and seal the seams. Trim any jagged edges and discard the scraps. Cut the pasta between each mound, separating the ravioli. Transfer the ravioli to the baking sheet and cover with plastic wrap. Repeat with the remaining pasta and filling. You should have about 32 ravioli.
Working in 2 to 3 batches so the ravioli don't stick to one another, cook the ravioli in the boiling water until they float to the surface and the dough is cooked through and tender, about 3 minutes. Transfer to the marinara sauce and serve topped with the Parmesan and basil.
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