Heat a small sauce pan with the olive oil and add the pieces of apple to it. Bake them quickly. You can now add the chestnuts, the star anise, cinnamon stick and maple syrup.
Add the orange juice and leave to simmer on low heat until the apple becomes soft. This is usually 15 minutes, depending on the type of apple. Add more orange juice if the pan becomes too dry.
Before serving remove the cinnamon stick and the star anise. Serve with coconut yogurt and chopped pistachio nuts.
If you want to make sure your chestnuts do not become too mushy, keep them away from the apples and prepare them in a separate pan. Heat this with some oil on high heat and quickly brown the chestnuts. Add them to the apple compote later.