In a blender, whirl crystallized ginger, fresh ginger, brown sugar, and vinegar until ginger is minced. Pour into a 2- to 3-quart pan and add 3/4 cup cream. Stir over high heat until boiling, then stir often until reduced to about 3/4 cup, 8 to 10 minutes; keep warm.
On each salad plate, lay a slice of toast; keep warm up to 10 minutes in a 150° to 200° oven.
With a hot thin-bladed, sharp knife (heat in hot water or over a burner), cut foie gras across narrow dimension into 1/2-inch-thick slices; wipe knife clean after each cut and heat again. Sprinkle slices lightly with salt and pepper.
Place a 10- to 12-inch nonstick frying pan over high heat; when it's hot enough for a drop of water to bounce off the surface, quickly lay foie gras slices in pan, filling it without crowding. Cook foie gras just until lightly browned on the bottom, 15 to 45 seconds, then turn slices and brown other sides (interiors will be warm, not hot), 15 to 45 seconds. Remove pan from heat, and with a wide spatula, quickly transfer equal portions of foie gras to toast; spoon fat in pan evenly over toast. Ladle ginger sauce equally around portions and garnish with chive spears.
Nutritional data is not available.