PREHEAT OVEN to 400 degrees Fahrenheit and place rack at center.
BUTTER + HEAT THE PAN: Butter generously a 10 - 11-inch (23cm) cast iron skillet and warm it over low flame. (You can use a 2-quart casserole, too. Warm it in the oven (or on stove over low heat if it's stoneware) with the butter and brush the melted butter around all over before adding the batter and baking.)
PIT THE PLUMS and cut in half. In a large bowl, toss the plums with ¼ cup of the sugar, saving the rest of the sugar for the batter. ADD THE PLUM HALVES WITH THE SUGAR cut-side down and evenly to the warm, buttered pan.
MAKE THE CLAFOUTIS BATTER: Combine the eggs, vanilla, brandy- if using, milk, the other ¼ cup (50 grams) sugar and a pinch of salt in a blender or food processor (or with a whisk by hand), blending a few seconds. Add the flour and blend until smooth, about one minute.
POUR THE CLAFOUTIS BATTER OVER THE PLUMS in the pan or casserole.
BAKE THE CLAFOUTIS: for about 30 minutes or until the center is set (small sharp knife comes out clean)and the edges are golden brown. Dust with powdered sugar. The dessert will at first be puffy but will naturally deflate or collapse as it cools. Slice in the pan and serve hot, warm, at room temperature or even cold the next morning for breakfast, should you be lucky enough to have leftovers. Store for up to 5 days, well-covered, in the refrigerator. Do not freeze.