• Preheat oven to 350°F (180°C). Lightly grease an 8-inch round cake pan or line it with parchment paper. You can also use a 9-inch round cake pan.
• Whisk together gluten-free all-purpose flour, baking powder, baking soda, and salt in a medium bowl. Set aside.
• In a large bowl, whisk the sugar and lemon zest together to release the lemon'snatural oils. Add the oil, eggs, buttermilk, and vanilla extract, and whisk until smooth and well combined.
• Add the wet ingredients to the dry ones and mix just until the batter is smooth. Avoid overmixing.
• Pour half of the batter into the prepared pan. Arrange half of the blackberries over the batter, then cover with the remaining batter. Add the remaining blackberries over the top, gently pressing them into the batter if needed.
• Bake for about 45–50 minutes, or until a toothpick inserted into the center comes out clean.
• Let the cake cool completely before removing it from the pan and frosting

For the blackberry cream cheese frosting:

• Place the blackberries in a small food processor and puree them. Press the puree through a fine-mesh strainer to remove the seeds.
• In a large bowl, beat the softened cream cheese and butter until smooth and creamy. Add the powdered sugar, vanilla extract, and blackberry puree. Mix on low speed until incorporated, then beat on medium-high speed until smooth and fluffy.
• If the frosting is too soft, add a little more powdered sugar until it reaches a spreadable consistency.
• Spread the frosting over the completely cooled cake.