Preheat the oven to 375 degrees F (190 degrees C). Grease a 10-inch pie plate, and sprinkle 1 tablespoon of sugar over the bottom.

Arrange plum halves, cut-side down, to cover the entire bottom of the pie plate. Sprinkle 2 tablespoons of sugar on top of plums.

To make the custard: Combine remaining 3 tablespoons of sugar, eggs, milk, flour, lemon zest, cinnamon, vanilla, and salt in a blender. Process until smooth, about 2 minutes. Pour over arranged plums in the pan.

Bake in the preheated oven until custard is firm and lightly browned, about 50 to 60 minutes. Let stand 5 minutes before slicing. Dust with confectioners' sugar before serving.