Preheat the oven to gas 4, 180°C, fan 160°C. Heat a griddle pan and brush the plums with half the melted butter. Put the plums in the pan (cut-side down) and cook for 3-4 minutes, until griddle lines appear. Transfer the plums to a baking tray (cut-side up) for roasting.
Put the shortbread in a sandwich bag and gently crush with a rolling pin until you have chunky crumbs. Add the rosemary and sugar and shake to combine.
Brush the plums with the remaining butter and drizzle over the amaretto. Top with the shortbread mixture and roast for 15 minutes, until soft and golden. Serve with crème fraîche or ice cream.