Preheat the oven to 350 degrees Fahrenheit. Grease an 8-inch round cake pan with vegan butter.
Cream the vegan butter and sugar with an electric mixer.
Add the eggs one at a time, beating after each.
Beat in the vanilla extract, almond extract, and coconut cream.
Use a high-speed blender to grind the pistachios until they are a flour-like consistency. Then spoon them into a bowl. No need to rinse it out just yet. Next, grind the oats until they resemble a flour-like consistency and add them to the bowl with the pistachio flour.
Mix the baking powder, cardamom, and salt with the pistachios, almond meal, and oats.
Then, add the dry ingredients to the wet ones and fold them in until all are incorporated.
Pour the batter into the pan and bake for 40 to 45 minutes. Remove from the oven and cool.
Mix the coconut milks with 2 tablespoons of homemade pistachio butter, and pour some into a large pie dish and save about 2 tablespoons. Then, remove the cake from the pan and add it to the pie dish with the pistachio milk. Then, pour spoonfuls of the liquid over the cake and let it soak in. Best served at room temperature.