Thinly slice the brown onions using a mandoline and soak them in water to reduce sharpness.
Blend the quartered onion, chopped carrot, and celery with extra virgin olive oil until smooth.
Cut the chuck steak and chicken rashers into small pieces.
Heat olive oil in a Dutch oven and cook the blended soffritto mixture for about 10 minutes.
Add the beef and chicken pieces to the pot, browning them over medium-high heat.
Season with salt and pepper, add bay leaves, cover, and simmer for 2 minutes.
Deglaze with white grape juice and cook uncovered for 5 minutes.
Add the sliced onions, season again, cover, and cook on low heat for about four hours.
After four hours, uncover and continue to cook for another two hours to reduce the liquid.
Shred the meat with a spoon and remove bay leaves before serving.
Cook ziti pasta according to package instructions and reserve some pasta water.
Combine the cooked ziti with the sauce, adding reserved pasta water as needed for consistency.