Preheat oven to 375 degrees F.
Recipe of Pate sablée
Beat butter and icing sugar until pale and creamy. Beat in egg. Add almond flour, and beat until just combined. (Frangipane can be refrigerated in an airtight container up to 1 week.)
Spoon frangipane into cooled tart shell, and smooth with a spatula. Let stand for 10 minutes. Bake until set, about 15 minutes. Let cool.
Prepare an ice-water bath. Bring a pan of water to a boil. Lightly score bottoms of apricots. Add apricots to boiling water, and blanch to loosen skins, about 1 minute. Using a slotted spoon, transfer to ice-water bath to stop the cooking, about 1 minute. Remove apricots, and gently peel. Cut in quarter, and remove pits.
Arrange apricots in concentric circles, sitting upright with the cut side on a slight angle.
Bake until browned, about 50 minutes. Let cool.
Remove the tart ring; dust with icing sugar and serve.