Preheat oven to 180ºC (356ºF). Line a round 8-inch baking pan with parchment paper, set aside. NOTE: Alternatively, if you have a non-stick pan, liberally grease it with melted butter and dust it with a light layer of flour. This will leave your finished cake with smooth sides.
In a medium size mixing bowl, add flour, baking powder, and salt. Whisk until well combined. Set aside.
In a large mixing bowl, using either electric hand beaters or a stand mixer with the paddle attached, add softened butter to the bowl.
Beat butter for a few seconds to break it up and it begins to turn creamy. This makes it easier on your beater when the sugar is added.
Add sugar and lemon zest. Beat with the butter for 2 minutes until pale and creamy. Scraping down the sides as needed.
Add eggs one at a time, beating for 10 seconds after each addition. Scrape down the sides as needed.
Pour in milk, oil, lemon juice, and vanilla. Beat for 15 seconds until well combined. Scrape down the sides again.
Add half of the dry flour mixture and beat until just combined. Scrape down the sides and add the remaining flour. Beat until incorporated, ensuring not to over-beat, just until the flour has combined then turn off the beater. If some excess flour is still visible around the sides of the bowl, gently fold it in with a spatula. If you over-beat, the cake can turn tough and dense after baking.
Add blackberries and gently fold through until combined, ensuring not to over-mix.
Pour into the lined pan and smooth out the top with a spatula.
Press a few extra blackberries on top of the cake batter.
Bake for 45-50 minutes, or until a skewer inserted into the middle comes out clean and it’s lightly golden all over.
Remove from oven and allow to cool in pan for 15 minutes.
Carefully remove from pan and transfer to a wire rack to cool completely.
To serve, dust a light layer of icing sugar if desired.
Serve and enjoy!