In a large (6 quart or larger) Dutch oven, heat olive oil over medium heat. Add onion, garlic, and mushrooms and season with salt and black pepper, to taste. Cook, stirring occasionally, until onions become soft and mushrooms begin to release liquids, approximately 4-5 minutes.
Add celery, carrots and ½ cup wine and continue cooking for 3-4 minutes.
Add crumbled beef and pork and stir to combine. Cook over medium heat until no longer pink inside. Remove from heat and carefully drain excess fat from pot, if necessary.
Set Dutch oven over low heat. Add tomato puree, petite-cut tomatoes, tomato paste, and remaining red wine to Dutch oven, along with oregano, thyme, rosemary, and honey. Season with additional salt and black pepper, to taste, and stir to combine.
Add bay leaves and Parmesan rind. Cover and simmer on low for 3-4 hours, stirring occasionally. If sauce becomes too thick, add a little water to achieve desired consistency.
Remove from heat and discard bay leaves and remaining Parmesan rind. Taste and adjust seasonings, as desired. Serve immediately with your choice of pasta or freeze for later use. Enjoy!