Bring the dairy-free milk to a gentle boil, then immediately remove it from the heat. Add the dried culinary lavender and allow it to steep for 2–3 minutes. Strain the milk into a heat-safe container to remove the lavender. Refrigerate the milk until fully cooled.

In a medium saucepan, combine the rinsed blackberries, maple syrup (or granulated sugar), and lemon juice. Place the pan over medium heat and stir until the mixture reaches a boil. Cook until the berries soften, then mash them using a silicone spatula or fork. Continue cooking until the jam thickens and reduces by approximately one-third, about 5 minutes. Allow the jam to cool completely before using.

Preheat the oven to 350°F (175°C). Line a 9×13-inch cake pan with parchment paper. Add the apple cider vinegar to the cooled lavender milk and return it to the refrigerator while preparing the batter.

In a large mixing bowl, whisk together the melted vegan butter, granulated sugar, dairy-free yogurt, and vanilla extract until smooth. Add the flour, baking powder, baking soda, and sea salt. While whisking, gradually pour in the lavender milk mixture. Mix only until the dry ingredients are fully incorporated.

Transfer the batter to the prepared cake pan. Place small dollops of blackberry jam on top of the batter. Using a butter knife, gently swirl the jam throughout the surface of the batter.

Bake for 50–55 minutes, or until a toothpick inserted into the center of the cake comes out clean and the top appears lightly golden.

Allow the cake to cool in the pan for 10 minutes. Then transfer it to a wire cooling rack and let it cool completely before frosting.

Prepare the vegan cream cheese frosting according to its recipe instructions. Add the blackberry jam and mix until fully incorporated. If the frosting becomes too soft, add the optional powdered sugar to stabilize it.

Spread the blackberry cream cheese frosting evenly over the cooled cake. Garnish with fresh blackberries if desired. Slice and serve.