Heat a large skillet over medium-high heat and add coconut oil and butter. Once melted, add in 4 pineapple rings and sprinkle brown sugar and salt over top. Cook until golden brown and caramely on both sides, about 5 minutes per side. Remove and let cool slightly.

Combine caramelized pineapple, coconut milk, yogurt, cardamom and cinnamon in a blender and puree until smooth. Pour into glasses and sprinkle a tiny bit of cardamom on top. Cut the remaining pineapple slice in half and add it to the top of the shake. Serve.