Preheat the oven to 350°F (175°C). Grease and line two 9-inch round cake pans (or 8-inch round cake pans) with parchment paper to make removal easy.
Zest the lemons until you get two tablespoons of zest. Then juice the lemons until you get 1/2 cup of lemon juice.
Stir together the almond milk the lemon juice and set aside until it curdles like buttermilk.
In a large mixing bowl, stir together the flour, baking soda, salt, and sugar until really well combined. Pour in the curdled buttermilk, olive oil, lemon zest, vanilla and poppy seeds. Use a large wooden spoon to mix the batter, just until the ingredients are combined. Avoid over mixing the batter, as it can cause the cake to become denser in texture.
Pour the batter evenly between the two pans (I use a kitchen scale to weigh each pan to evenly distribute the batter). Arrange the cakes in the middle rack of the oven and bake for 30-35 minutes until the center is set, and a toothpick inserted comes out with only a few moist crumbs. I baked mine for 32 minutes (you will need to bake them for a few minutes longer if using 8-inch cake pans).
Remove the cake pans from the oven and allow to cool for 10 minutes in the pan, then transfer the cakes to a wire rack to cool completely before inverting them onto the cooling rack.
To make the Blackberry Ginger Jam: Add the blackberries, ginger, maple syrup, and lemon juice to a small saucepan over high heat. Bring the mixture to a boil. After 2-3 minutes, use the back of a wooden spoon or a fork to break down and mash the berries. Cook for 7-10 minutes or until the jam has reduced and thickened a little bit. Remove from the heat and then stir in the chia seeds to thicken. The jam will also thicken as it cools.
To make the Vegan Cream Cheese Frosting: To a large mixing bowl, add the softened butter and cream cheese. Beat on low speed with an electric handheld mixer (or stand mixer) until smooth and creamy. Beat in the vanilla and lemon zest for a few seconds. Gradually add the sifted powdered sugar in 1 cup increments, and mix on low speed until the icing is thick and spreadable. If your frosting is too runny, place the bowl in the freezer for 10-15 minutes.
To assemble the cake: If you are making this into a traditional layer cake, you’ll need to slice each cake layer in half, horizontally, so you end up with four cake layers (see notes above underneath “Layering the cake” for tips). Spread 1/4 of the frosting over the first cake layer using a frosting spatula or silicone spatula, then spread 1/4 of the jam on top. Repeat with the remaining three cake layers. If you have any leftover frosting, lightly spread the frosting on the outside of the cake. If you don’t want to make this into a four-layer cake, simply add a generous amount of the frosting and jam on top of the first cake, top with the second cake, and then repeat.