Prepare Onions: Cut the brown onions in half and slice thinly using a mandoline or onion slicer. Soak the slices in a bowl of water to reduce sharpness and prevent tears.
Make Soffritto: Roughly chop 1/4 brown onion, carrot, and celery. Blend with a generous amount of extra virgin olive oil and a splash of water until smooth.
Prepare Meat: Cut chuck steak and pork rashers into small, even-sized chunks. Do not trim fat as it adds flavor.
Cook Soffritto: Heat a Dutch oven or large pot over medium heat. Add about 3 tablespoons of extra virgin olive oil and the blended soffritto. Cook for about 10 minutes, stirring occasionally, ensuring it does not dry out (add water or oil if needed).
Brown Meat: Add the meat to the soffritto and stir to combine. Increase heat to medium-high and brown the meat for 5-10 minutes until fat starts to melt and liquid forms at the bottom.
Steam Meat: Cover with a lid and cook on medium-high heat for 2 minutes to allow steam to help cook the meat and release flavors.
Season and Add Bay Leaves: Add salt and pepper sparingly. Stir and add 4 bay leaves. Cover and simmer for another 2 minutes.
Deglaze with White Wine: Pour in white wine to deglaze the pan. Cook uncovered for about 5 minutes to allow alcohol to evaporate.
Add Onions and Slow Cook: Add the soaked sliced onions on top of the meat. Stir gently to combine. Add salt and pepper generously. Cover with lid and cook on low heat for 4 hours, stirring gently every 30 minutes.
Reduce Sauce: Remove lid and continue cooking on low heat for 2 more hours to reduce liquid and create a thick, gem-like sauce, stirring occasionally.
Finish Sauce: Remove bay leaves before serving. Use a wooden spoon to gently squash the sauce to combine meat and onions into a rich, tender mixture.
Cook Pasta: Boil water with a generous tablespoon of rock salt. Cook ziti pasta until al dente, stirring occasionally to prevent sticking.
Combine Pasta and Sauce: Drain pasta and toss with desired amount of Genovese sauce. Add Pecorino Romano cheese off the heat and toss again.
Serve: Serve immediately with additional Pecorino if desired. Leftover sauce can be frozen and reheated gently on the stove (avoid microwave).