Step 1 Heat the oven to 400 degrees. Cut a slit into the thickest part of each fish fillet just large enough to insert a basil leaf in each. Season with salt and pepper. Put the fish, skin side up, on a baking sheet and set aside.
Step 2 In a large saucepan, heat 2 teaspoons olive oil over medium-low heat. Sweat the leeks, carrots and fennel for 5 minutes, then add the artichoke, onions and celery and continue to cook the vegetables for 15 minutes. Add the chicken stock and bring it to a boil. Reduce heat and simmer 10 to 15 minutes, until the carrots are tender. Add the zucchini and the haricots vert; cook 1 minute. Stir in the garlic and pasta. Season to taste with salt and pepper. Turn the heat off and keep covered so that it stays warm until ready to serve.
Step 3For the pistou, rinse 6 cups basil leaves under cold water. Pat them dry on paper towels and put them through a salad spinner to remove excess moisture. Put the basil leaves in a blender or food processor with the remaining one-half cup olive oil, garlic clove and salt to taste. Puree until smooth. Set aside.
Step 4Bake the fish fillets in the oven for about 5 minutes or until the fish tests done in the center; they should be firm to the touch. When ready to serve, divide the minestrone among four soup bowls and place one fish fillet in each bowl. Sprinkle around the diced tomato and ham. Spoon four small dollops of the pistou into each bowl. (You will have extra.) Thinly slice the remaining basil into a chiffonade and sprinkle over each fillet.