Microwave the water until hot. Add the dried mushrooms and let rehydrate for 10 minutes. Using a fine mesh strainer set over a small bowl drain the mushrooms making sure to reserve the liquid. Set aside.
In a small skillet over medium heat cook the wine until it has reduced to about 2 tablespoons, about 20 minutes. Set aside.
While the wine is reducing use a food processor to finely grind the rehydrated porcini mushrooms. Add the carrot and pulse until the carrot pieces are smaller than a chop, but larger than a mince. Add the onion and pulse until combined.
Heat a large pot over medium high heat. Melt the butter then stir in the mushroom, carrot and onion mixture. Cook until the vegetables are soft.
Add the sugar and minced garlic and cook for 30 seconds. Add the ground beef and cook for 1 minute, making sure to break apart the meat with a wooden spoon. Stir in the milk and continue breaking apart the meat. Once the milk begins to bubble, reduce to medium low heat.
Continue to cook the ground meat, making sure to break up the meat often, for 20 minutes. Once the meat has begun to sizzle, stir in the tomato paste to combine. Add the can of crushed tomatoes, reserved mushroom liquid, ¼ teaspoon salt and ⅛ teaspoon pepper.
Cook for another 15 minutes then stir in the reduced wine. Cook for a couple more minutes then remove from the heat. Serve hot over pasta or store in the fridge for 2 days or the freezer for 2 months.
Recipe by Lemon & Mocha at http://www.lemonandmocha.com/2014/01/16/beef-bolognese-sauce/