Preheat oven to 350°. Wash the zucchini thoroughly under running water and remove stems. In a large pot, bring salted water to a boil. Add the whole zucchini and cook over medium heat for 10 minutes. Drain and cool. Cut a lengthwise strip (1/4 inch) from each zucchini; mince the strips and set aside. Carefully scoop the flesh from each zucchini and discard. Drain zucchini on paper towels.
In a large skillet over low heat, cook the onion in 3 TBS olive oil just until soft. Add the minced zucchini strips and continue cooking, covered for 5 minutes. Add the garlic, basil, anchovy paste and 1/4 cup bread crumbs. Season with salt and pepper. Blend thoroughly and cook for additional 2-3 minutes. Fill the hollowed-out zucchini with the mixture and place in an ovenproof casserole that has been brushed with 1 TBS olive oil. Bake at 350 degrees for 10 minutes. While the zucchini is baking, toast the remaining bread crumbs in 2 TBS olive oil. Cool slightly and mix with the grated Asiago. Remove the baked zucchini from the oven and turn on the broiler. Sprinkle the bread crumb and Asiago mixture over the zucchini and place the dish under the broiler until the crumb mixture is golden brown. 6 servings.