Melt the butter in an 8-inch cast-iron skillet over medium-high. Sprinkle the plum halves evenly with the sugar and place, cut-side down, in the skillet.
Cook until the cut sides are golden in color, 2 to 3 minutes. Reduce heat to medium, turn the plums over, and cook until tender, 5 to 6 minutes more.
Transfer the plums to a plate, leaving the juices behind. Add the maple syrup to the skillet and stir. Combine the plums and plum syrup. Keep warm. (Or refrigerate for up to 2 days; warm before using.)
Divide the yogurt among 4 bowls. Top each with 2 plum halves and chopped walnuts. Drizzle with the syrup.
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