Preheat oven to 170degC.
Grease a 20cm square cake tin and line with a strip of baking paper that overhangs the sides (to help remove the cake after baking).
In a large bowl, beat olive oil with the sugar and vanilla.
Beat in the eggs and lemon zest.
Beat in the soured milk (make this up a few minutes in advance).
Add the flour and salt, and beat in until just combined.
Spread the batter into the prepared baking pan.
Place the apricot halves on top, cut side down (4 rows of 5 halves, some slightly overlapping, works well in my tin), and push in a little.
Bake for 40 minutes or until golden brown.
Cool in the tin until firm enough to handle, then lift out using baking paper strip and finish cooling on a wire rack.