Wash artichokes. Trim off stems to 1 inch or less and trim loose outer leaves. Trim tips of remaining leaves, if desired. Cook artichokes, covered, in a large amount of boiling salted water for 20 to 30 minutes (depending on size) or until a leaf pulls out easily. Invert artichokes to drain. (To prevent discoloration, do not use aluminum or cast iron pans; use stainless steel, nonstick-lined, or enamel-coated cookware.)
When cool enough to handle, halve each artichoke lengthwise. Pull out the prickly purple-tipped leaves in the center of each artichoke to expose the fuzzy choke. Using a small spoon or a melon baller, scrape out the choke and discard.
In a medium saucepan melt margarine or butter. Add carrot, onion, parsley, dried basil (if using), garlic, and pepper; cook over medium heat until tender, stirring occasionally. Remove from heat. Stir in bread crumbs and snipped fresh basil (if using). Spoon the vegetable mixture in the center of each artichoke half.
Place artichokes in a 2-quart square baking dish. Pour boiling water around the artichokes to a depth of 1/2 inch. Cover loosely with foil. Bake in a 400 degree F. oven for 15 to 20 minutes or until heated through. To serve, carefully remove artichokes with a slotted spoon to serving plates. Garnish with fresh basil, if desired. Makes 4 side-dish servings.