01 - Preheat the oven to 350°F. Grease and flour an 8-inch round cake pan.
02 - In a bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until evenly distributed.
03 - In a separate large bowl, beat the softened butter and granulated sugar together until the mixture is light and fluffy.
04 - Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully incorporated.
05 - Stir the finely chopped fresh basil into the wet mixture, distributing it evenly throughout.
06 - Alternately add the dry ingredient mixture and the milk-yogurt blend to the wet ingredients, beginning and ending with the dry. Mix until just combined to avoid overworking the batter.
07 - Pour the batter into the prepared cake pan and smooth the top with a spatula for an even surface.
08 - Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
09 - While the cake cools, combine the mixed berries, granulated sugar, and lemon juice in a small saucepan over medium heat. Cook for 8 to 10 minutes, stirring occasionally, until the berries soften and the mixture thickens slightly. Remove from heat and cool completely.
10 - Beat the cold heavy cream until soft peaks form. Add the powdered sugar and finely chopped basil, then continue beating until stiff peaks hold their shape.
11 - Spread the basil whipped cream evenly over the completely cooled cake. Spoon the berry compote over the top just before serving for the freshest presentation.