Soak the mushrooms in 1 ½ cups warm water for 10 minutes or until softened. Reserve 1 cup soaking water. Chop the mushrooms.
Heat a 12-inch skillet over medium-high heat. Add the beef and season with salt and pepper. Cook until well browned, stirring often to separate meat. Pour off all but 1 tablespoon fat.
Add the carrots, onion and garlic to the skillet and cook for 5 minutes or until the vegetables are tender-crisp, stirring often. Add the wine, reserved water and softened mushrooms and cook for 3 minutes. Stir in the tomato puree and heat to a boil.
Reduce the heat to low. Cook for 30 minutes, stirring occasionally. Season to taste with salt and pepper. Stir in the basil, if desired, during the last 2 minutes of the cooking time. While the sauce is cooking, cook and drain the pappardelle according to the package directions.
Serve the pappardelle with the sauce. Top with the cheese and additional basil, if desired.