Preheat oven to 350 degrees F. Line a cupcake pan with 12 liners.
Mix together oil, sugar, coconut milk, orange juice, and vanilla.
In separate bowl combine flour, turmeric, baking powder, baking soda, and salt.
Add dry ingredients to wet ingredients and mix till just combined. Add orange zest and mix. Bake for 15 to 18 minutes.
In a saucepan whisk together all ingredients except orange zest. Place over low heat and whisk for 5 minutes while mixture heats up. Keep cooking for 5 to 10 more minutes until the curd starts to thicken. Turn off heat and let cool.
Skim coconut cream off the top of the chilled can of coconut milk. Place in stand mixer fitted with whisk attachment. Whisk till coconut cream gets light and fluffy. Add powdered sugar, coconut oil, and orange zest and continue to whisk. Use immediately.
Use a serrated knife to cut a hole in the middle of each cupcake. Spoon as much curd as you can into the center of each cupcake. Top each cupcake with a spoonful of frosting.