Preheat oven to 350 degrees F. Line a 9-inch square cake pan with parchment paper, or coat well with cooking spray, and set aside.

Rinse strawberries and blueberries and set aside together in a small bowl.

Combine the sugar and lemon zest in a large bowl. Rub the mixture lightly between your fingertips for about 1 minute, so that the sugar is infused with the lemon scent.

Crack the eggs into the sugar mixture. Whisk until the mixture is smooth and buttery yellow, then pour in the buttermilk, oil, lemon juice, and vanilla extract. Whisk again until smooth.

Sprinkle the flour, baking powder, and salt on top of the batter. Fold with a spatula until mostly smooth; it will start out a little lumpy, but even out.

Add most of the berries, reserving a few to sprinkle on top of the cake. Fold gently two or three more times, then scrape the batter out into the pan and spread into an even layer. Scatter the reserved strawberries and blueberries on top.

Bake for 40-50 minutes, until a toothpick or sharp knife inserted into the center comes out clean. Let the cake cool for about 10 minutes in the pan.

If you lined the pan with parchment, you can use the edges of the parchment to lift the cake out and set on a wire rack to cool completely, then cut. Otherwise, I recommend leaving the cake in the pan and serving from there.

Cut squares and serve with dollops of whipped cream or a dusting of powdered sugar and extra berries on top. Enjoy!