Preheat the oven to 400°F (200°C). Arrange the plums, cut-side down, on a small rimmed baking sheet. Roast until the plums are tender and their juices begin to emerge, about 10 minutes.
Meanwhile, in a small saucepan over medium heat, stir together the ginger, sugar, and 2 tablespoons water and bring to a gentle simmer. Cook until the flavors have blended and the liquid becomes lightly syrupy, about 5 minutes.
Divide the warm plums among small bowls. Drizzle with the ginger syrup, top with dollops of yogurt or whipped cream, and serve.