Combine 4 tablespoons coconut oil, 1 egg, 1 tablespoon honey and 1 teaspoon vanilla extract in the bowl of a food processor; pulse until well combined. Add 120g ground almonds and oats gradually to the mixture; pulse until well combined and a dough is formed.
Roll out dough to fit a 23cm tart tin. Bake pastry case in the preheated oven until edge of pastry is golden, 10 to 15 minutes.
Place water, 80ml honey, cinnamon and 1 teaspoon vanilla extract in a saucepan; bring to the boil. Add plums; simmer over medium-low heat until softened, about 20 minutes.
Combine 175g ground almonds, 3 eggs, 120ml coconut oil and remaining honey in a blender; blend until smooth. Pour over pastry case. Place plums and raspberries carefully on top.
Bake in the preheated oven until set, about 30 minutes.
You could also make 4 mini individual tarts with this pastry recipe.