Scoop pulp out of zucchini halves, leaving a 1/4-inch border, using a spoon. Chop pulp and set aside.

Place zucchini shells, cut-side down, in a large skillet; pour in water. Cover skillet and bring to a boil; reduce heat and simmer until zucchini are slightly tender, about 5 minutes. Drain water from skillet and turn zucchini shells over in the skillet and sprinkle with salt.

Heat margarine in a separate skillet over medium heat; cook and stir zucchini pulp and tomato in the melted margarine until tender, about 3 minutes. Stir eggs, walnuts, 1/4 teaspoon salt, pepper, and basil into tomato mixture; cook, lifting thickened portions with spatula to let uncooked portions of egg flow to bottom, until eggs are set but still moist, 3 to 5 minutes.

Spoon egg mixture into zucchini shells. Sprinkle Cheddar cheese over egg mixture and cover skillet. Cook over low heat until cheese melts, about 2 minutes.