To prepare the lamb, trim off any fat. Cut the lamb into 1-inch cubes and pat dry. Heat the olive oil in a dutch oven over medium high heat. Add a few of the lamb pieces to the dutch oven being careful not to crowd the pan. Allow to sear until browned on one side. Flip the lamb and brown the other side. Remove the lamb to a plate and set aside. Repeat until all the lamb is browned, adding a bit more olive oil to the dutch oven if it looks dry.
Once all the lamb is browned, turn the heat down to medium low. Add the diced onions, fennel, and carrots and sauté for about 4 to 5 minutes until they soften and begin to brown.
When the vegetables have softened, add the minced garlic, tomato paste, fennel seeds, kosher salt, and pepper. Sauté for another minute until the garlic is fragrant. Add the crushed tomatoes, red wine, and beef broth along with the rosemary and bay leaves.
Return the lamb along with any accumulated juices to the braising liquid and bring to a boil. Reduce the heat, cover, and allow to simmer gently on low for 2 to 2 1/2 hours until the lamb is tender. Periodically skim the braising liquid and remove any excess fat or foam that rises to the top.
The lamb is done when it is extremely tender and can be pulled apart. To make this easier, use a slotted spoon to remove the pieces of lamb and then shred the meat. Return the lamb to the braising liquid. Taste the ragu, adding more seasoning if needed.
When the lamb is nearly finished, cook the rigatoni. Place a large pot of water on high heat and bring to a boil. Add a generous amount of salt to the water. Add the rigatoni to the boiling water, stirring occasionally to prevent the pasta from sticking.
Remove the rigatoni from the heat when it is almost fully cooked but still has a bit of bite to it. The rigatoni will finish cooking in the ragu. Use a spider strainer to scoop the rigatoni into the ragu, reserving some of the pasta water. Turn the heat up to medium high and gently stir the pasta into the ragu. Allow to cook for a few minutes until the ragu thickens and begins to cling to the pasta. If the mixture looks dry, add a splash of pasta water.
When the pasta is fully cooked and the sauce has thickened, remove from the heat. Add the finely grated Parmesan and stir to combine. Serve the pasta with more grated Parmesan and enjoy!