How to Make It
In a large bowl, toss the beef chuck with the onions, garlic, thyme sprigs, bay leaves, pure olive oil and 1 cup of the red wine; season with salt and pepper. Cover with plastic wrap and refrigerate overnight.
Drain the meat. Transfer the meat to a paper towel–lined plate and pat dry; reserve the onion mixture separately.
In a medium heatproof bowl, cover the dried porcini with the port. Microwave at high power for 1 minute, until the porcini are softened; let cool. Using a slotted spoon, transfer the porcini to a food processor. Add the tomato paste and half of the porcini soaking liquid and process until smooth. Reserve the remaining porcini soaking liquid.
In a large, heavy casserole, heat 2 tablespoons of the extra-virgin olive oil. Add the bacon and cook over moderately high heat until crisp, about 5 minutes. Add the reserved onion mixture and the celery and cook over moderately high heat, stirring occasionally, until softened, about 8 minutes. Using a slotted spoon, transfer the onion-bacon mixture to a bowl.
Heat the remaining 2 tablespoons of olive oil in the casserole. Dust the meat with flour, shaking off any excess. Add half of the meat to the casserole and cook over moderately high heat until browned all over, about 10 minutes. Transfer the meat to the bowl with the onion-bacon mixture. Lower the heat to moderate and brown the remaining meat.
Return all of the meat and the onion mixture to the casserole and stir until sizzling. Add the porcini paste and stir for 1 minute. Stir in the carrots and sliced shiitake caps. Add the stock, the remaining red wine and the remaining porcini soaking liquid and bring to a boil. Season with salt and pepper. Cover and simmer over low heat until the meat is tender, about 2 hours. Discard the thyme sprigs and bay leaves.
Uncover the stew and cook over moderate heat until the sauce is slightly thickened, about 10 minutes. Add the parsley and 2 teaspoons of chopped thyme, season with salt and pepper and serve.