Bring orange juice or apple juice to a boil in a small pan. Stir in dried fruit and remove the pan from heat. Cover and let stand until fruit is softened or about 15 minutes, then drain.
In a medium mixing bowl, stir together sour cream or yogurt, cream cheese, and a ¼ cup of the finely snipped basil.
Spread cream cheese mixture evenly on each tortilla. Sprinkle with softened fruit. Near the edge of each round spread prosciutto. Tightly roll the bread, starting from the edge closest to the meat. Wrap each roll in plastic wrap. Chill for 4 to 24 hours.
Cut each roll into 1 inch slices. Garnish with additional basil leaves or orange slices.