To prepare the sweet tart crust, add ½ cup of butter andsugar to the bowl of a stand mixer. Beat for 2 minutes, until the mixture islight and fluffy. Add the eggs, vanilla, and salt and mix to combine again.Gradually add the flour, mixing until just combined. Remove the dough from thebowl, form into a disc, and wrap in plastic wrap. Place in the refrigerator for1 hour.
Preheat the oven to 350 degrees F. Grease the sides andbottom of an 8-inch fluted tart pan with the remaining 1 teaspoon of butter.Set aside.
Lightly dust your worksurface and rolling pin with flourand roll out the sweet tart crust until it is ½-cm thick. Transfer to thegreased tart pan and gently press the dough into the sides and bottom of thepan. Trim the excess dough and place the tart in the refrigerator to chill for 15 minutes.
Once chilled, remove the tart from the refrigerator andused a fork to dock the bottom of the tart several times to prevent rising.Place in the center of the oven and bake for 15 minutes.
Remove the cooked tart shell from the oven and spread ¼cup of apricot jam on the bottom of the tart. Arrange the halved plums inconcentric circles on top of the apricot jam and sprinkle the sugar on top ofthe plums. Return the tart to the oven and bake for 25 to 30 minutes, or untilthe plums have softened.
Remove the tart from the oven and let it cool for 10minutes before glazing the plums with the remaining ¼ cup of apricot jam usinga pastry brush. Let cool completely before slicing and serving.