For the ricotta cavatelli: Combine the ricotta, eggs and salt in a large bowl, then stir in the flour. Gently combine with your hands to bring together into a dough. Knead the dough together, adding additional flour until the dough is firm and not sticky. Tightly wrap in plastic and rest in the refrigerator for at least 1 hour and up to overnight.
Cut the dough into quarters. Working with one quarter at a time, roll the dough on a lightly floured surface into a 1/4-inch-thick rope. With a knife, cut the rope into 1/2-inch pieces. Use a bench scraper or your index and third fingers held together to gently press down on each piece, beginning at the top and moving down toward the bottom, dragging the bench scraper toward you and causing the pasta to roll over on itself. Transfer the formed pasta to a lightly floured baking sheet and let dry at room temperature for at least 30 minutes.
For the lobsters: Bring 3 gallons salted water to a boil and add the juice of the lemon.
Place the lobsters in a large, deep roasting pan or pot and pour the boiling water over the lobsters. After 3 minutes, remove the lobsters and pull off the tails. Place the body, claws and legs back in the hot water for 5 more minutes. Separate the meat from the shells. Cut the meat into chunks and reserve.
For the pomodoro sauce: Place a saucepot over medium heat and add the olive oil. Add the onions, garlic and a large pinch of salt. Cook, stirring occasionally, until the vegetables soften, 8 to 10 minutes. Stir in the chile flakes and tomatoes and season with salt and pepper. Tie the oregano and thyme together with a piece of butcher twine, then add it to the sauce. Bring to a simmer and cook over medium-low heat, about 30 minutes. Remove the herb bundles, transfer the sauce to a blender, let cool slightly and puree on low speed to preserve the color of the sauce. Pour the sauce back into the pot.
Bring a large pot of salted water to a boil. Cook the cavatelli until it floats to the top, 3 to 4 minutes.
Add the pasta to the pomodoro with 1/4 cup of the pasta water and the lobster chunks. Stir and toss to coat the pasta in the sauce, then add the butter, whole basil leaves and a drizzle of olive oil. Continue to toss the pasta until it is well coated and glossy.
Serve with freshly grated Parmesan over the top and another drizzle of olive oil.
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