Preheat oven to 180C/350F. Grease and line the bottom of a 23cm/11inch round pan.
With a stand mixer or hand held mixer whisk together eggs, sugar, olive oil and vanilla until thick and pale, about 5 minutes.
Slowly incorporate the lime juice and zest.
With the mixer on low alternately add flour and milk in three batches. Mix until on just combined. Don't overbeat.
Pour the cake batter into the prepared pan and evenly sprinkle blueberries over the surface.
Bake for 1 hour.