Wash artichokes and trim stems. Place artichokes in a microwave-safe casserole with water. Micro-cook, covered, on 100 percent power (high) for 7 to 9 minutes or until a leaf pulls out easily. Drain and cool.
Discard small outer leaves of 1 cooled artichoke. Pull off large leaves; cover and chill leaves until serving time. Pull out the tender leaves from the center as a single clump. Remove the fuzzy choke by scooping it out with a spoon; discard the choke. Finely chop the artichoke heart.
In a blender container or food processor bowl combine cheese, sour cream, capers, and basil. Cover and blend or process until smooth, stopping occasionally to scrape down sides. Stir in the artichoke heart. Cover and chill until serving time or up to 24 hours.
To serve, remove center leaves, choke, and heart from remaining artichoke. Spoon dip into center, spreading outer leaves. If desired, garnish with additional capers and a Belgian endive leaf. Arrange artichoke leaves and other vegetables around dip. Makes about 1-1/2 cups dip (twenty-four 1-tablespoon servings).