Heat the oven to 180C/160C fan/gas 4. Butter and line the base and sides of two 20cm sandwich tins.
Beat the butter and sugar together in a large bowl with an electric whisk for 8-10 mins, or until pale and fluffy. Add the eggs one at a time, beating well after each addition. Sift in the flour, baking powder and salt, and fold in using a large metal spoon. Add just enough of the milk to create a dropping consistency.
Divide the batter between the prepared tins and smooth the tops with a spatula. Bake on the middle shelf of the oven for 25-30 mins, or until golden and firm to the touch. Leave to cool slightly in the tins, then transfer to a wire rack to cool completely.
Meanwhile, make the filling. Spoon the conserve into a small pan and stir in the apricots and whole thyme sprigs. Warm over a low heat for 2 mins until loosened, then transfer to a heatproof bowl and leave to cool and infuse for 1-2 hrs.
Whip the cream with the icing sugar and vanilla until the mixture just holds its shape (be careful not to overwhip – see tip, below).
Remove and discard the whole thyme from the conserve mixture and stir in the thyme leaves. Spread the mixture over one of the sponges, then top with the vanilla whipped cream and sandwich with the remaining sponge. Dust the cake with some icing sugar. Will keep in the fridge for up to three days.