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In a large stock pot, add your olive oil, then heat to medium high heat. When hot, add ground beef. Season with salt and pepper and cook until browned.
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Add mushrooms, onions, and tomato paste and cook until onions start to soften about 3-5 minutes. Add garlic cloves and cook until fragrant, about 30 seconds. Add balsamic vinegar and stir well to scrap the flavor bits off the bottom of the pot.
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Add tomatoes, parmesan cheese, Italian seasoning, salt and pepper. Stir well. Reduce heat to low. Cook uncovered for at least two hours, stirring occasionally to prevent sticking. The longer you cook, the better.
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Half an hour before serving, add milk or half and half and stir well. Continue to cook.
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Serve over pasta. Sauce tastes delicious the next day and stores well in the fridge for up to three days. Freeze any leftover.