Preheat the oven to 375°F (190°C).

In a small saucepan over medium heat, melt the butter and cook, swirling occasionally, until it smells nutty and toasted and the milk solids turn golden brown, 3 to 4 minutes. Remove from the heat immediately and cool completely.

Brush the bottom of a 10-inch/25-cm round baking pan or dish with butter. Add the plums in an even layer to the baking pan.

In a blender, combine the cooled browned butter, milk, heavy cream, eggs, flour, ¼ cup (50 grams) of the sugar, and the salt. Blend for 1 minute. Gently pour the mixture over the plums, and sprinkle with the remaining 1 tablespoon of sugar.

Bake until the top is lightly browned and the custard is just set, 35 to 40 minutes. Serve warm or at room temperature. Leftover clafoutis will keep, covered, in the refrigerator for up to 3 days.