If you like, top the apricots with fresh herbs, such as mint or basil, in addition to the pistachios.
Preheat broiler. Place sugar in a small saucer. Dip cut side of apricots in sugar to coat and transfer to a small broilerproof baking dish. Broil, rotating once, until apricots are caramelized and juicy, 3 to 4 minutes.
Remove apricots from oven. Let cool slightly and top with ricotta and pistachios. Serve immediately.
Heat Meets Sweet Apricots are full of heart-healthy beta-carotene. Caramelizing them under the broiler makes their flavor and aroma even more complex.