For a charcoal grill, place plums, cut sides down, on the rack of an uncovered grill directly over medium-hot coals. Grill for 5 to 8 minutes or until plums are tender and lightly browned. (For a gas grill, preheat grill. Reduce heat to medium-high. Place plums on grill rack over heat. Cover and grill as above.) When cool enough to handle, slice plums.
In a small bowl, combine mascarpone cheese and the 1 tablespoon honey.
Spread mascarpone mixture over browned side of a flatbread. Add plums and sprinkle with almonds and ginger before returning flatbread to the grill. If desired, drizzle with additional honey before serving. Cut into wedges. Makes 6 appetizer servings.