Preheat oven to 400 degrees F. In a large bowl, whisk together melted butter, eggs, buttermilk, brown sugar, sugar, vegetable oil, coconut cream, vanilla extract, and coconut extract. Whisk until smooth.
In a separate bowl, whisk together kosher salt, baking powder, cornmeal, all-purpose flour, and shredded coconut. Add to wet ingredients and mix until smooth, about 10-15 seconds
Spray a 10-inch oven-safe skillet with nonstick baking spray and add batter to the skillet. Sprinkle with additional coconut shreds and bake for 35 minutes, until golden brown.
To make the lime butter, combine butter, lime zest, lime juice, sugar, and salt in a small bowl and mix together. Spread on top of a slice of coconut cornbread.