Preheat the oven to 350 degrees (for meatballs only). Dice onion and chop garlic then set aside.
Season all meats generously with coarse salt and ground pepper.
Drizzle about half of the olive oil in a dutch oven to coat it generously. On med/high heat, sear all meat (including meatballs) in batches 2-3 min per side, adding more oil if needed. Be careful not to overcrowd the pot when browning. Remove meats and set aside.
Quickly turn heat to low, and drain off the excess oil. Deglaze the dutch oven with your favorite red wine, then add the canned tomatoes, tomato paste, and beef broth back into the pot. Stir to combine.
Place the meatballs on a sheet pan. Finish cooking JUST the meatballs in the oven for 20-30 min at 350 degrees, or until the internal temperature reaches 160 degrees. Let them cool when finished and then refrigerate until the very end.
In a separate fry pan on medium heat, use the remaining olive oil to coat the pan. Saute the onions for 4-5 min. (or until clear), then add garlic and cook for 1-2 more minutes (being careful not to burn).
Pour sauteed onions and garlic into the dutch oven with the sauce. Using a stick blender, blend the tomato sauce and onion so that the sauce is not lumpy.
Add all meats (except meatballs), the carrot, and about one cup of water back into the sauce. Cover and simmer on low for several hours, stirring occasionally. Check to make sure meats have reached a safe internal temperature.
Skim oil off the top, then season to taste. Add cooked meatballs during the last 10min. minutes of cooking.
To serve, spoon Sunday Gravy sauce with meat over spaghetti squash, pasta, or zoodles. Cut up the meats and garnish with freshly grated parmesan cheese and/or basil if desired.