Heat oven to 400°F. Grease an 8-inch square pan with a dab of coconut oil; line with parchment if you like.
Whisk cornmeal, flour, sugar, baking powder, and salt in a large bowl. Stir in shredded coconut.
In a second bowl, whisk coconut milk, beaten eggs, melted coconut oil, and vanilla until smooth.
Pour wet mixture into dry ingredients. Stir gently until just combined; do not overmix.
Scrape batter into the prepared pan and smooth the top.
Bake 22–26 minutes, until the top is golden and a toothpick comes out clean from the center.
Cool in the pan for 10 minutes. Slice into squares and serve warm.