Step 1 To make light vegetable stock: Remove the dark outer leaves and the dark green tops of the leeks and rinse them well. Cut the dark green tops and outer leaves in 1- or 2-inch slices and put them in a medium saucepan. Add the parsley stems, one-fourth cup of the sliced carrot and water to cover, about 3 cups. Cover and bring to a boil, then reduce the heat to a simmer and cook for 30 minutes. Remove from heat and strain the stock, discarding the solids.
Step 2 Halve the white and light green parts of the leeks lengthwise and rinse them well. Cut the leeks into thin slices, about one-eighth inch thick; you should have about 2 1/2 cups.
Step 3Heat 2 tablespoons olive oil in a sauté pan or deep, medium-size skillet (about 9 1/2 inches wide) over medium-low heat. Add the leek slices and sprinkle with salt and pepper to taste. Cover and cook, stirring often, until the leeks are tender, about 10 minutes. Transfer the leeks to a bowl.
Step 4To peel the tomatoes: In a medium saucepan, boil enough water to generously cover the tomatoes over high heat. Prepare a bowl with enough ice water to cover the tomatoes. Core the tomatoes and slit the skin at the bottom of each in an X. Put the tomatoes in the boiling water and boil just until the skins start to pull away from the X, about 30 seconds. Transfer the tomatoes to the bowl of ice water. Remove the tomatoes from the cold water promptly and pull off the peel with the aid of a paring knife. Halve the tomatoes, squeeze out their juice and seeds, and chop the tomatoes; you should have about 2 cups.
Step 5Add 1 tablespoon oil to the sauté pan and heat it briefly over low heat. Add the remaining carrot pieces. Cook, stirring occasionally, for 3 minutes. Add the minced garlic and cook, stirring, until it is fragrant, about 15 seconds. Add one-half cup vegetable stock, cover and bring to a boil. Simmer the mixture over low heat until the carrot pieces are tender, about 5 minutes. Add the chopped tomatoes, a pinch of salt, a pinch of pepper, the bay leaf and the thyme. Cover and bring to a simmer. Cook over medium-low heat, stirring occasionally, until the tomatoes are tender and the sauce thickens slightly, about 5 minutes. If the sauce becomes too thick to moisten the fish, add 2 to 3 tablespoons vegetable stock.
Step 6Add the fish pieces to the sauce, drizzle them with 1 tablespoon olive oil and sprinkle them lightly with salt and pepper. Cover and cook over low heat for 3 minutes. Carefully turn the pieces over, sprinkle them lightly with salt and pepper and cook until the thickest part of a fish piece becomes opaque in the center, 3 to 5 minutes; check with the point of a sharp knife. Using a fish spatula or slotted spatula, carefully transfer the fish pieces to a plate.
Step 7Stir one-fourth cup of the leek mixture into the sauce. If you would like a thicker sauce, simmer it uncovered over medium-high heat, stirring often, for 3 minutes, or until it