Preheat your oven to 350°F (175°C) and prepare a muffin tin with cupcake liners.

Mix ground flax with three tablespoons of water in a small bowl; let sit for about 5-10 minutes to thicken.

In a large bowl, whisk together all-purpose flour, cornstarch, baking powder, and salt.

In a separate bowl, whisk vegetable oil, sugar, canned coconut milk, orange juice, orange zest, and vanilla extract until smooth.

Add the thickened flax mixture to the wet ingredients and stir gently.

Gradually fold in the dry ingredients into the wet mixture until just combined.

Fill the prepared liners about two-thirds full and bake for 18-20 minutes until a toothpick comes out clean.

Let cupcakes cool in the tin for 5 minutes before transferring to a wire rack to cool completely.

For the frosting, cream vegan butter until smooth, then add powdered sugar, orange juice, and zest until fluffy.

Frost the cooled cupcakes and enjoy!

Store leftovers in an airtight container at room temperature for up to three days.