Chop about ⅓ of the strawberries for the cake batter and set them aside. Slice or chop the remaining strawberries for the topping, and set them aside.
Preheat oven to 180°C/360°F and adjust a baking rack onto the middle shelf. Grease and dust with flour (or line with parchment paper) a 9-inch cake pan and set it aside.
In a large bowl, place the eggs and sugar. Beat the mixture with an electric whisker until light and pale, then gently whisk in the olive oil, lemon juice and zest, and mix until all the ingredients are combined.
Place a sieve/ strainer over the bowl. Add flour and baking powder, and sift into the cake batter. Whisk until just combined (do not overmix).
Add the chopped strawberries to the batter and mix until just combined.
Pour the cake batter into the prepared baking pan. Top the batter with the remaining strawberries.
Bake in the oven for approximately 40 minutes. During the last 10 minutes of baking time, cover the top of the cake with foil to prevent it from browning too much. To check if the cake is ready, insert a toothpick in the center, if it comes out clean, the cake is ready.
Remove the cake from the oven, allow to cool, then gently remove the cake from the pan.
Dust your Italian Strawberry Cake with powdered sugar and serve at room temperature. It's lovely topped with vanilla ice cream, fresh cream, or Greek yogurt.
