Step 1Soak the cod overnight in cold water to cover, changing the water a few times.
Step 2Rinse the cod and cut it into three or four pieces. Place the cod in a large saucepan and cover it with fresh cold water. Add the parsley, thyme, bay leaf, onion, garlic and peppercorns. Heat it slowly until the first white foam appears at just under a simmer. Remove from the heat, cover and let stand for 10 minutes.
Step 3Using a slotted spoon, remove the pieces of cod to a plate and reserve the cooking liquid for the potatoes. Let the cod stand until cool enough to handle, then remove the bones and skin from the fish; flake the flesh and keep warm.
Step 4Meanwhile, cook the potatoes in the poaching liquid just until tender, 10 to 15 minutes. Drain the potatoes and dry them in the saucepan over low heat. Immediately mash them until smooth, using a ricer or a masher. Beat in one tablespoon of the walnut oil, the beaten egg and the chopped garlic. Beat until smooth and keep warm.
Step 5Meanwhile, scald the milk in a small saucepan and heat the remaining walnut oil in a second saucepan.
Step 6Place the flaked cod and a little of the warm milk in a food processor. Pulse on and off once. Gradually add the warmed oil and milk alternately, pulsing without overworking the cod.
Step 7Scrape the fish into the potatoes. Season with pepper to taste and reserve.
Step 1Heat a broiler. With a paring knife, hollow out the top half of the tomatoes. Tie a length of kitchen twine tightly around the tomatoes, finishing with a bow or knot.
Step 2Season the tomatoes with a little salt and pepper and let them drain upside down on a paper towel.
Step 3When ready to serve, spoon 2 tablespoons of the chopped arugula into the hollowed tomatoes. Spoon the salt cod mixture on top of the arugula, creating a nice mound over the top of the tomatoes.
Step 4Grind a little black pepper over the top and place the stuffed tomatoes on a baking sheet under the broiler until the cod puree is golden and the tomatoes are heated through, about 3 minutes. Remove the string from the tomatoes. Put the stuffed tomatoes on a plate and sprinkle over chopped parsley.