Preheat the oven to 180°C C. Grease and line a 22 x 22 cm - baking tray.
In a large mixing bowl beat the butter, sugar and vanilla until light and fluffy.
Add one egg at a time, alternating with 1Tbsp of flour.
Fold in gently the rest of the flour, then add the ground almonds, lemon zest and milk. Mix gently with a wooden spatula.
Transfer the batter to the baking tray, spreading it out evenly.
Scatter the berries on the top, pushing them into the batter - they should be flush with the top of the batter. Sprinkle almond flakes over it, enough to cover it completely.
Bake in the oven for about 30 minutes until light brown.
Turn off the oven and open its door. Let the cake cool in there for 5 minutes, then transfer it to a wire rack. When completely cool, cut it into slices or squares.