In a medium bowl combine carrots, cream cheese, mayonnaise and ginger paste; add salt and pepper.
Spread one side of each piece of bread lightly with butter. Top the buttered side of 2 slices of bread with carrot/ginger mixture (about 1/4-inch thick). Top with alfalfa sprouts and then remaining bread slices, buttered side down.
Carefully cut the crusts from each sandwich with a sharp knife. Cut the sandwiches in half diagonally and then cut in half again. Yields 2 whole sandwiches, 4 halves or 8 fourths.