Dough: Place the flour in a large in a large mixing bowl and stir to mix well. Make a well in the center of the flour and add the water a little at a time, stirring well with your hands until the dough comes together. You may need more or less water, depending on the humidity of your kitchen.
Place the dough on a floured work surface and knead it like bread for 8 to 10 minutes, until smooth and elastic. Cover and let stand for 10 minutes at room temperature.
Roll the dough into long dowels about ¾ inch thick. Cut into flat disks about ¼ inch to ½ inch thick. Press the center of each disk with a thumb to form a saucer shape. Set aside under a dish towel until ready to cook.
Condiment: In a large skillet or Dutch oven, heat 2 tablespoons olive oil over high heat. Place the sausage in the pan and cook until fat has been rendered, moving occasionally to avoid sticking. You will have to dump the rendered fat once or twice to avoid deep-frying the meat in its own fat. Remove the meat and set aside. Remove the excess fat from the pan, reduce the heat to low, and add the onion, carrot, and celery. Sweat the vegetables over low heat until tender, letting them get soft but not browned, for about 6 minutes. Add the red wine and scrape the bottom of the pan with a wooden spoon as you stir the wine in to dislodge browned bits of meat. Add the tomatoes, bring the mixture to a boil and return the sausage to the pan. Reduce to a simmer and cook for 30 to 45 minutes, until the mixture is at ragu consistency. Add more liquid if necessary to keep the meat moist.
Prepare the pasta dough according to the recipe
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12- to 14-inch sauté pan, heat 3 tablespoons olive oil until almost smoking. Add the garlic, chili flakes and broccoli and toss over high heat until broccoli is tender, about 4 minutes. Add the ragu and toss over high heat for 2 minutes, seasoning with salt and pepper to taste.
Drop the orechiette into the boiling water and cook until tender yet al dente, about 2 minutes. Drain the pasta and add it to the pan with the broccoli and ragu. Toss over high heat one minute, divide evenly among 6 warm pasta bowls, grate Pecorino Toscano over each bowl and serve immediately.