Put the onions, fennel, celery, and garlic in a food processor and puree to a coarse paste.
Coat a wide, deep, pan with olive oil, add the puréed veggies, season with salt, and bring to medium-high heat. Cook the veggies until all the liquid has evaporated and they begin to stick to the pan—you want to brown the crap out of these guys until crud starts to form on the bottom of the pan. Stir occasionally to scrape up the brown bits, then let the crud form again Be patient here and don’t rush it—this is where the big flavor develops—it will take up to 30 minutes.
When the lovely brown crud has formed and been scraped down a couple of times, add the tomato paste, stirring to combine. Let it start to brown a little and continue stirring for 2 to 3 minutes. There’s not much liquid at this point to keep things from burning, so be careful and move fast. Add the wine, stir to combine, and scrape up any remaining brown bits; cook until about half the wine has evaporated, 4 to 5 minutes. Add both the sweet and spicy sausage and, using a spoon to break it up, cook until the meat is brown (this is where another round of big brown flavors is formed, so take your time), 10 to 15 minutes.
Add enough water to the pan to cover the meat about ½ inch. Stir to combine well and add the bay leaves, and the thyme bundle. Taste, season with salt, and taste again—it’s by no means done, but it should taste good. Bring the sauce to a boil and reduce to a simmer. Continue cooking, checking occasionally, for 3 hours, tasting, seasoning, and adding more water as needed.
During the last half hour of the cooking process, bring a large pot of well-salted water to a boil. Add the pasta and cook for 1 minute less than the instructions on the package suggest. Taste it: It should be toothsome with just a little nugget of hard pasta still in the center—this is al dente. Drain, reserving ½ cup of the pasta cooking water. Remove the thyme bundle and bay leaf from the sauce. Then remove half of the ragù from the pan and reserve.
Immediately add the cooked pasta to the pan with the ragù and toss to combine, adding more of the reserved ragù or pasta water if needed; continue cooking for another couple of minutes, until the pasta and sauce cling together and the liquid has reduced. Remove the pot from the heat and add the Parmigiano and a generous drizzle of the olive oil. Toss the pasta and sauce vigorously—this is the marriage of the pasta and sauce, and the cheese and olive oil are the glue that holds this lovely relationship together.