Preheat the oven to 180C/350F/Gas 4. Line a baking tray with baking parchment.
In a bowl, rub the flour and butter together using your fingertips until the mixture resembles breadcrumbs.
Stir in the apricots and sugar.
Gradually add the beaten egg and stir until the mixture comes together as a soft dough. If the mixture becomes too sticky, add a little more flour.
Turn out the dough onto a lightly floured work surface. Cut it into six equally sized pieces and roll each into a ball. Arrange the balls onto the prepared baking tray.
Bake the buns in the oven for 15-20 minutes, or until golden-brown on top and cooked through (a skewer inserted into the centre of each should come out clean). Set aside to cool, then eat with grapes, if desired.