Preheat oven to 350°F. Lightly butter an 8-by-8 baking dish and place on a rimmed baking sheet.

Spread halved apricots out evenly in the bottom of the baking dish and sprinkle with light rum.

In a blender, combine eggs, heavy cream, granulated sugar, lemon zest, vanilla, fine grain sea salt and flour. Process until smooth and incorporated. Pour the batter over the apricots.

Bake until the clafoutis is puffy, golden brown on top and firm to the touch (40 - 45 minutes). The center should be completely set. Let the clafoutis cool slightly before serving. Finish with a dusting of confectioners sugar on top.