How to Make It
Make the meatballs In a small saucepan, melt the butter. Add the flour; cook over moderate heat, whisking, until a thick paste forms, 1 minute. Gradually whisk in the milk and cook until thick, 2 to 3 minutes. Scrape into a large bowl and let cool slightly. Add the chuck, pork, eggs, parsley, wine, garlic, paprika, 2 teaspoons of salt and 1 teaspoon of pepper; mix well. Cover and refrigerate for about 2 hours.
Form the meat mixture into 1 1/2-inch balls. In a large saucepan, heat 2 tablespoons of the oil. Dredge half the meatballs in flour. Cook over moderately high heat, turning, until browned all over, about 8 minutes. Transfer to a plate. Repeat with the remaining 2 tablespoons of oil and meatballs; don’t wipe out the pan.
Make the sauce Grate the tomato halves on the large holes of a box grater set in a bowl until only the skins remain; discard the skins.
Add the onion, carrot, garlic and a generous pinch of salt to the saucepan and cook over moderate heat, stirring occasionally, until just starting to brown, about 8 minutes. Add the tomatoes and paprika and simmer over moderate heat until slightly reduced, 3 to 5 minutes. Stir in the flour, then stir in the wine and brandy and simmer until barely thickened, 5 minutes. Transfer to a blender and puree until very smooth. Return to the saucepan, whisk in the stock and bring to a boil. Season with salt and pepper.
Add the meatballs to the sauce, cover and simmer over moderately low heat until cooked through, about 15 minutes. Uncover and simmer until the sauce is slightly thickened, about 5 minutes. Stir in the parsley, cover and keep warm over very low heat.
Meanwhile, make the mushrooms In a large skillet, heat 2 tablespoons of the oil until shimmering. Add half the mushrooms; season with salt and pepper and cook over moderately high heat, stirring occasionally, until browned, 8 minutes. Transfer to a bowl. Repeat with the remaining oil and mushrooms.
Spoon the meatballs and sauce into bowls, top with the mushrooms and serve.