Heat 1 TBSP of olive oil in a medium size skillet over medium heat. Add the onion and cook until translucent, about 4 minutes. Add 2 cups of the chopped mushroom, reserving the rest for the sauce, if making. If not making the sauce, add all the chopped mushroom here. Cook, stirring, until it releases and reabsorbs some of its liquid, about 5 minutes. Let the mushroom mixture cool.
Place the bread and milk in a small bowl and let soak for 5 minutes. Drain, squeeze out the excess liquid, and finely crumble the bread.
Place the crumbled bread and the veal, pork, pancetta, egg, applesauce, parsley, paprika, pepper, salt, and the mushroom mixture in a large bowl. Gently knead the meatball mixture with your hands just until all the ingredients are thoroughly combined; do not over-knead.
Spread a thin layer of flour on a large plate. Wet your hands, then break off a piece of the meatball mixture and shape it into a 1 inch ball. Dust the meatball in the flour, shaking off any excess, then gently toss it between cupped hands to give it shape. Repeat with the remaining meatball mixture, placing the floured meatballs on a small baking sheet.
Heat 1 TBSP of the olive oil in a very large skillet, preferably nonstick, over medium-high heat. Add half of the the meatballs and brown all over, shaking the skillet so that the meatballs brown evenly. If you plan to serve the meatballs in the sauce, cook them for 3 to 4 minutes. If serving without sauce, cook them until cooked through, about 7 minutes, adjusting the heat so that the meatballs don't burn.
Using a slotted spoon, transfer the meatballs to a bowl. Add the remaining 1 TBSP of olive oil to the skillet and cook the remaining meatballs in the same fashion. If serving the meatballs without the sauce, let them cool 5 to 10 minutes, then sprinkle with chopped parsley and serve with crusty bread. If you are making the sauce, don't clean out the skillet.
Almond and Saffron Sauce Heat 1 TBSP of the olive oil in the skillet over medium heat. Add the onion and cook until translucent, 2 to 3 minutes. Add the reserved chopped mushrooms and cook for 2 minutes. Add the tomato and cook, stirring, until it begins to caramelize, 6 to 7 minutes. Add the sherry and wine, increase the heat to high, and cook for 1 to 2 minutes. Add the chicken stock, stir, then stir in the meatballs. Reduce the heat to very low, cover the skillet, and cook for 10 minutes.
Meanwhile make the picada Heat the remaining 2 TBSP olive oil in a small skillet over medium heat. Add the bread cubes and cook until they begin to brown, about 2 minutes. Add the garlic and almonds and cook until fragrant and just beginning to brown, about 1 1/2 minutes.
Using a slotted spoon, transfer the bread, garlic, and nuts to a food processor. Add the parsley and saffron and pulse until mixture is ground.
Gently stir the picada into the skillet with the sauce. Cook until the sauce is flavorful, 2 to 3 minutes. Remove the skillet from the heat and let cool, 5 to 10 minutes. Garnish with additional parsley and serve with crusty bread.