Combine all tomato ingredients. Set aside to steep and let flavors combine for about 1/2 hour.
Combine goat cheese, butter and chives.
Spread goat cheese mixture on bread slices and place on a baking sheet lined with a silpat. Sprinkle Parmigiano Reggiano on top. Bake in preheated 425 oven till cheese is bubbly and golden brown (about 10 minutes). Place toasts on serving platter or plates.
Top toasts with tomato mixture. Sprinkle more Parmigiano Reggiano on top, if you wish.