Combine 1/4 cup coconut oil, 1 egg, 1 tablespoon honey, and 1 teaspoon vanilla extract in the bowl of a food processor; pulse until well combined. Add 1 cup ground almonds and oats gradually to the mixture; pulse until well combined and a dough ball is formed.
Roll out dough to fit a 9-inch pie dish.
Bake in the preheated oven until edge of crust is golden, 10 to 15 minutes.
Place water, 1/3 cup honey, cinnamon, and 1 teaspoon vanilla extract in a saucepan; bring to a boil. Add plums; simmer over medium-low heat until softened, about 20 minutes.
Combine 1 cup ground almonds, 3 eggs, 1/2 cup coconut oil, and remaining honey in a blender; blend until smooth. Pour over pastry. Place plums and raspberries carefully on top.
Bake in the preheated oven until set, about 30 minutes.