Make the dough: On a clean work surface, mound the flour. Create a deep well in the center and add the eggs and olive oil. Using a fork, beat the eggs and oil. Then, starting from the interior wall of the well, gradually incorporate the flour into the wet ingredients as if scrambling eggs, until a thick batter-like consistency forms. Use a bench knife or bowl scraper to cut and fold the remaining flour into the center until a shaggy mass forms; press it to form a dough.
With clean dry hands, move the dough and any remaining scraps and flour to a clean work surface. Sift flour lightly over the board, then knead the dough until semi-smooth, about 3 minutes. Scrape the work surface of dried flakes and continue to knead dough gently until it is smooth and supple and springs back when poked, and most or all of the flour is incorporated, about 15 minutes more. (If dough is dry and tight, wrap in plastic and let rest 5–10 minutes before continuing to knead.) Wrap the ball tightly in plastic and refrigerate at least 1 hour or ideally 1 day.
Meanwhile, make the filling: Set a fine sieve over a medium bowl. Add the ricotta, then press it through the sieve with a spatula. Add the ½ cup pecorino, sugar, cinnamon, nutmeg, and egg; season with salt. Mix thoroughly, then pack into a piping bag fitted with a round tip, and refrigerate until needed, up to 3 days.
Make the ragù: Crush 1 garlic clove. In a medium saucepan over medium-high heat, add the tomatoes, garlic clove, 1 tablespoon olive oil, and marjoram; bring to a boil. Lower the heat and gently simmer until slightly reduced, 12–15 minutes. Set aside.
Mince the remaining 3 garlic cloves. In a large pot over medium heat, add the remaining oil. Once hot, add the garlic, sage, rosemary, crushed red pepper, and fennel pollen if using; cook, stirring, for 30 seconds. Add the onion, celery, fennel, and carrot and raise the heat to medium-high; cook, stirring occasionally, until softened, 12–15 minutes. Stir in the lamb, breaking it up into small pieces; season with salt and pepper. Cook, stirring occasionally, until no pink remains, about 5 minutes. Add the wine and cook until reduced slightly, 2–3 minutes. Remove the garlic and marjoram from the tomato sauce and discard. Add the tomato mixture and the chicken stock to the lamb; bring to a boil, then reduce the heat to maintain a simmer. Cook until the meat is tender and the sauce is reduced by half, about 3 hours.
Shape the cazini: Using a mattarello or rolling pin, roll out the dough as thinly as possible into a large circle at least 20 inches in diameter (see pg. 99). Using a 2¾-inch biscuit or round cookie cutter, cut out rounds as close as possible to one another. Pipe scant 1 teaspoon balls of filling into the center of each, then fold one side of each round over the filling to cover. Press down firmly and all over the edges to seal well. (If inside edges of pasta do not stick together easily, spritz very lightly with water from a spray bottle.)
Bring a large pot of salted water to boil. Meanwhile, reheat the lamb ragù if needed. Gently add the cazini to the boiling water and stir immediately. Cook until the pasta floats to the top and is al dente, 1½–2 minutes. Remove with a spider or slotted spoon to a serving bowl or platter. Add 2 tablespoons pecorino and some spoonfuls of ragù to taste; toss gently to coat, adding 1 to 2 tablespoons of pasta water if needed to loosen the sauce. Garnish with more pecorino and serve immediately.