Position a rack in the center of the oven and heat the oven to 300°F.
Put the can of tomatoes and their juices in a food processor and process until puréed. Using a spatula or the back of a ladle, press the purée through a medium-mesh sieve set over a bowl to remove the seeds
Pat the lamb shanks dry with paper towels and season generously with salt and pepper. Spread the flour in a wide, shallow dish and dredge the shanks lightly in the flour.
Heat 1/4 cup of the oil in a 7- to 8-qt. Dutch oven over medium-high heat. Add the shanks and cook, turning a few times, until they are golden brown on all sides, 8 to 10 minutes. Transfer the shanks to a large plate, discard the fat, and clean the pan with paper towels.
Heat the remaining 1/4 cup oil in the pan over medium heat. Add the onion and cook, stirring frequently, until it's pale gold and soft, about 5 minutes. Add the garlic, bay leaf, and pepper flakes, stir for 1 minute, and add the bell peppers. Cook, stirring frequently, until the peppers begin to color and soften a little, 4 to 5 minutes.
Return the shanks to the pan and stir them around with the pepper mixture. Increase the heat to high, add the wine, and stir until the wine is reduced approximately by half, 1 to 2 minutes. Add the tomatoes, 3/4 cup of broth, and 1/2 tsp. salt. Stir until the liquid begins to simmer.
Turn off the heat, cover the pan tightly with a lid or heavy-duty aluminum foil, and put it in the oven. Cook, turning the shanks every half hour or so, until the meat begins to fall off the bone, 2 to 2-1/2 hours.
Remove the pan from the oven and transfer the shanks to a cutting board. When the shanks are cool enough to handle, pull the meat off the bones, discarding any fat and connective tissue. Cut the meat into bite-size pieces. Stir the meat into the sauce and bring it back to a gentle simmer. Cook, stirring a few times, until the sauce has a medium-thick consistency and a rich, reddish color, 5 to 10 minutes. If the sauce seems too dry, stir in some or all of the remaining broth. Discard the bay leaf, adjust the seasoning with salt, and turn off the heat.
The ragù keeps for up to 5 days in the fridge and up to 1 month in the freezer. Transfer the hot ragù to a large bowl and refrigerate it, uncovered, stirring well every 20 minutes, until its completely cool. Cover the bowl tightly with plastic and refrigerate it, or freeze it in small containers or zip-top bags.
Once you've made your rich ragù, all that's left is to combine it with pasta. To serve four to six people, you'll need 4 cups ragu, 1 Tbs. unsalted butter, 1 lb. dried or fresh pasta (cooked and drained), and 1/2 cup freshly grated Parmigiano-Reggiano or Pecorino Romano. Heat the ragù (either in the Dutch oven you used to cook it or in a 12-in. skillet, if reheating) over medium-high heat. Add the butter and then pour in the pasta and Parmigiano or pecorino. Toss over medium-high heat until the pasta and sauce are well combined. Serve immediately.
Short, full-bodied dried pastas like rigatoni and orecchiette work great with ragù, because their nooks and ridges capture the sauce. If you want to use fresh pasta, a wide shape like papperdelle can stand up to a hearty sauce. And a ragù is a good excuse to cook gnocchi, too.too.