In a large Dutch oven, combine the butter and oil. In a food processor, pulse the onion, celery and carrot until roughly chopped, about 5 pulses. Transfer to the Dutch oven. One can at a time, add the tomatoes with juices to the food processor and puree until smooth; transfer to a medium bowl. Add half the beef to the food processor and pulse until coarsely ground, 5 to 10 pulses, then transfer to another medium bowl; repeat with the remaining beef. Repeat with the pork, in batches, adding it to the beef. Finally, process the pancetta to a coarse paste, about 30 seconds; add to the other meats.
Set the pot over medium-high and cook, stirring occasionally, until the vegetables are lightly browned, about 5 minutes. Stir in the tomato paste and cook, stirring, until the paste begins to brown, about 5 minutes. Add the wine and cook, scraping up any browned bits, until the pot is almost dry, about 1 minute. Stir in the ground meats, then stir in the broth, tomatoes, bay and pepper flakes. Bring to a simmer, then partially cover, reduce to medium-low and cook, stirring occasionally, until the meat is tender, the sauce is thick and the volume has reduced to about 8 cups, 2½ to 3 hours. Remove the pot from the heat.