Put the pine nuts and water in a high speed blender (such as a Vitamix); process until smooth and creamy. Set pine nut “cream” aside.
To a food processor, add the carrots; pulse several times to finely chop. Set carrots aside. Add the mushrooms to the food processor and pulse several times until finely chopped. Set mushrooms aside.
Heat the oil in a large heavy skillet over medium-heat. Add the garlic, shallots and carrots; sauté for 5 to 6 minutes, or until vegetables are soft. Add the mushrooms and saute 3 to 4 minutes, or until mushrooms are soft. Season with oregano and salt and pepper to taste. Transfer vegetables to a 5 or 6 quart slow cooker.
Heat the skillet over medium heat, add the ground beef. Season with salt and pepper to taste. Cook until meat is no longer pink, about 3 minutes. Pour the wine into the skillet and cook until liquid evaporates. Stir in the pine nut cream, tomato paste and tomato sauce, season with additional salt and pepper to taste and simmer for 5 minutes.
Transfer the meat mixture to the slow cooker along with the vegetables. Gently stir the meat and vegetables together. Cook on high for 2 hours or on low for 4 to 5 hours. Let Bolognese sit 30 minutes before serving. Serve warm.