Place the onions, garlic, carrot and celery in the bowl of a food processor fitted with the metal blade; pulse until finely minced but not puréed.
Heat 2 tablespoons of the olive oil in a large pot over medium-high heat. Add the ground beef into the pan and cook, stirring occasionally and breaking the beef into small pieces, until slightly browned but not cooked all the way through, about 5 minutes. Using a slotted spoon, transfer the partially cooked beef to a plate. Set aside.
Add the remaining tablespoon olive oil to the pan, reduce the heat to medium, and add the minced vegetables. Cook, stirring frequently, until the vegetables are very soft, 6 to 8 minutes. Do not brown; reduce the heat if necessary.
Add the wine; continue cooking, stirring to scrape any brown bits from the bottom of the pan, until the wine is mostly absorbed by the vegetables, a few minutes.
Add the tomatoes, cream, salt, pepper, sugar, thyme and bay leaves and bring to a boil. Reduce the heat and simmer, covered, until the sauce is thickened, about 20 minutes.
Add the ground beef back to the pan and continue simmering, covered, until the sausage is fully cooked and the flavors meld together, about 10 minutes. Taste and adjust seasoning if necessary. Fish out the bay leaves and discard.