Preheat oven to 350°F with a rack in the center. Lightly grease an 8" round pan and line the bottom with a parchment round. 

Combine the pistachios and 1 tablespoon of the flour in a food processor. Pulse until the pistachios become a coarse meal. The flour helps absorb the pistachios oils and keeps the mix from blending into pistachio butter. 

In a medium bowl, whisk together the remaining flour, ground pistachios, sugar, baking powder, baking soda, salt and lemon zest. 

In a large mixing bowl, whisk the eggs and olive oil until thick, creamy and smooth. Whisk in the milk, 2 tablespoons of juice from the lemons and vanilla. Then, gradually whisk the dry ingredients into the wet until just combined.

Pour the batter into the prepared pan and bake for 35 to 40 minutes, until the cake is warm golden brown on top and springs back when gently pressed. 

Allow the cake to cool in the pan sitting atop a wire rack for 30 minutes. Run an offset spatula around the edge of the cake to help release it from the pan. Then turn the cake out onto the rack, and allow it to cool completely for at least another 30 minutes to 1 hour.

Strawberry Topping

While the cake cools, combine the sliced strawberries, sugar and vinegar in a medium bowl and gently toss to mix. Set aside for 30 minutes to allow the berries to macerate and create a thick syrup. 

Whipped Cream Topping

Meanwhile, make the whipped cream. Either using a handheld or stand mixer fitted with a whisk attachment, whip the heavy cream, powdered sugar and vanilla extract on a medium-high speed until medium peaks form. It should take about about 3–4 minutes. Alternatively, you can do this the old fashioned way and use a whisk and large metal bowl to whip the cream by hand. Hot tip, chill the metal bowl and whisk in the freezer before whipping the cream to speed up the process.

Top and Serve

There are two different routes to take when assembling the Strawberry Pistachio Olive Oil Cake. It all depends on how you plan to serve and enjoy the cake.

Party style. If you are planning to present the cake for a party or event and want to share a showstopping, then a fully assembled cake is the way to go. Top the entire cake with a billowy blanket of fresh whipped cream. Then, pile the citrus vinegar scented strawberries right on top and sprinkle with coarsely chopped pistachios. For the prettiest and freshest presentation, assemble the layers just before serving. However, the cake will remain well preserved when fully assembled in the fridge for a number of hours.

Single serving style. If instead you plan to take this Strawberry Pistachio Olive Oil Cake down over the course of a couple of days, I advise dressing it as you go. Prepare all of the elements ahead of time and store the whipped cream and macerated berries in a sealed container. Then slice of wedges and top fresh with whipped cream, strawberries and a handful of chopped pistachios. Assembling as you go will keep the cake at optimal freshness levels.