Salt & Straw owners Kim and Tyler Malek know how to make a mean bowl of pasta.
Preheat the oven to 350°. Season the lamb with salt and pepper. In a deep heavy pot, heat the oil over medium-high. Add the lamb and cook until browned, about 2 minutes per side. Transfer to a plate. Add the chopped fennel and garlic to the pot and cook, stirring often, until soft, about 5 minutes. Add the stock and bring to a boil. Return the lamb to the pot. Cover and transfer to the oven. Cook until the meat is tender, about 2 hours. Uncover and let the lamb cool in the braising liquid.
Using tongs, transfer the lamb to a medium bowl. Strain the broth into a large bowl. Transfer the fennel and garlic to the bowl with the lamb. Using 2 forks, shred the meat, fennel, and garlic together. Add the lamb filling to the bowl with the broth. Cover and refrigerate overnight.
On a work surface, mix the flour and 1 tsp. salt. Form a large well in the center of the flour. Crack the eggs into the center, then add the olive oil. Using your fingertips or a fork, gradually mix the flour into the eggs until incorporated. Knead until the dough is shiny and smooth, 5 to 10 minutes, adding a spoonful of water if needed to help the dough come together (the dough will be firm). Shape the dough into a ball and wrap in plastic wrap. Let the dough rest at room temperature for 30 minutes or refrigerate up to 48 hours.
Divide the dough into 4 pieces; cover each piece with plastic wrap. Using a pasta machine and working according to the manufacturer’s instructions, run 1 piece of dough through the pasta roller, starting with the widest setting and gradually working down to the thinnest setting, creating long, thin sheets of pasta. Cover the pasta sheets with plastic wrap to keep them from drying out. Repeat with the remaining pieces of dough
Place 1 sheet of pasta on a lightly floured work surface; cut it in half crosswise. Place rounded teaspoonfuls of the lamb filling down the center of 1 of the pieces of pasta, spacing the mounds about 1 inch apart. Top with the other piece of pasta, pressing around each mound of filling to seal. Using a large round cookie cutter, cut between the mounds of filling to create ravioli. Repeat with the remaining pasta and filling.
Bring a large pot of water to a boil. Salt the boiling water. Working in batches, cook the ravioli until al dente, 2 to 3 minutes. Using a slotted spoon, arrange the ravioli on a platter. Top with crème fraîche, Parmesan, and fennel fronds.