Rinse the raisins and place them in a bowl of water along with the prunes to soak for at least 10 minutes, then drain and set aside.
Meanwhile, take the pre-soaked salt cod fillets and remove any pin bones using fish tweezers. (If using dry salted cod, desalt it first by soaking it in a large bowl of cold water in the refrigerator for about 48 hours, changing the water approximately every 6 hours).
Finely chop the thyme leaves and parsley; set aside for seasoning later.
Peel and finely chop the shallot. Gently sweat it in a wide pan or skillet with the olive oil over low heat for 8–10 minutes, then add the minced garlic.
Add the salt cod fillets, chopped thyme, and white wine, and cook for 5 minutes. Pour in the tomato purée and stir gently with a wooden spoon. Season with salt and pepper to taste, cover with a lid, and simmer over moderate heat for an additional 20 minutes.
Peel the potatoes and slice them into 2–3 mm rounds using a mandoline; place them in a bowl of cold water as you slice them to prevent discoloration. Drain the potatoes, add them to the pan with the cod, and cook for approximately 30 more minutes. Meanwhile, toast the pine nuts in a separate dry skillet until lightly golden.
Halve the prunes to remove the pits (if any) and cut them into slices. Add the raisins, prunes, and chopped herbs to the cod, then simmer for another 5 minutes to allow the flavors to meld.
Transfer to serving plates and garnish with the toasted pine nuts before serving.
