Preheat the oven to 350 F. Line and 8-inch square baking pan with parchment paper and set aside.
In a large bowl combine 2 cups flour with the shredded coconut and brown sugar. Whisk to combine. Add the butter and coconut oil.
Using a pastry blender, cut butter and coconut oil into flour until mixture resembles large peas. Add the ice water, 1 tablespoon at a time, while kneading the dough. Continue to knead until a dough forms.
Evenly press the dough into the prepared pan and bake for 20 minutes.
Meanwhile, in a medium sized bowl combine remaining flour with the sugar, lime juice, lime zest, tequila, eggs and fine salt. Whisk until fully incorporated.
Remove the crust from the over and pour the lime mixture over the hot crust. Return to the oven to bake for an additional 20 minutes.
Transfer the pan to a cooling rack, sprinkle with rock salt and let stand until room temperature. Refrigerate until ready to serve.