Place cèpes in a small bowl, cover with hot water and set aside until soft, about 10 minutes, then drain, rinse, and finely chop. Reserve 12 whole squid. Finely chop remaining squid bodies. Heat 2 tbsp. oil in a medium skillet over medium heat. Add shallots and cook until fragrant, about 3 minutes. Add garlic, cèpes, and white mushrooms and cook, stirring, for 5 minutes, then add tomatoes and parsley. Cook, stirring, for 2 minutes more then stir in chopped squid. Cook until squid is firm, about 1 minute, then remove from heat, season with salt and pepper, and set aside to cool.
Place lobster stock in a small saucepan and bring to a boil over high heat. Add veal stock and reduce by two-thirds, about 10 minutes. Reduce heat to medium-low, stir in butter, season with salt and pepper, and keep warm.
Spoon 2–3 tbsp. squid mixture into each reserved body, pinning closed with a toothpick. Heat 2 tbsp. oil in a large skillet over medium-high heat. Cook stuffed squid, in batches, turning frequently, until golden, 3–6 minutes. Transfer to a large plate, cover with aluminum foil, and set aside. Wipe out skillet, add remaining oil, and sauté reserved tentacles until firm, about 1 minute. Remove toothpicks, arrange 3 stuffed squid on each plate, spoon sauce around, and garnish with tentacles and parsley sprigs if desired.