Preheat the oven to 375℉. Butter a 10-inch pie plate and sprinkle 1 tbsp granulated sugar over the bottom.
Arrange the plum halves, cut side down, so that they cover the entire bottom of the pie plate. Sprinkle 2 tbsp of sugar over the top of the plums.
In a blender, combine the remaining 3 tbsp of sugar, eggs, milk, flour, lemon zest, cinnamon, vanilla and salt. Process until smooth, about 2 minutes.
Pour the custard over the fruit.
Bake for 50-60 minutes in the preheated oven, or until firm and lightly browned. Let stand 5 minutes before slicing. Dust with confectioner's sugar before serving.