Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang on two sides to lift the bars out later. Lightly spray the parchment with nonstick cooking spray.
nonstick cooking spray, parchment paper
In a medium bowl, whisk together the melted butter, 1/2 cup granulated sugar, 1 teaspoon vanilla, and 1/2 teaspoon fine sea salt until smooth. Add 2 cups flour and 1 cup unsweetened shredded coconut, then stir with a spatula or wooden spoon until a soft dough forms. It should look slightly crumbly but hold together when pressed.
1 cup unsalted butter, 1/2 cup granulated sugar, 1 teaspoon pure vanilla extract, 1/2 teaspoon fine sea salt, 2 cups all-purpose flour, 1 cup unsweetened shredded coconut
Transfer the crust dough to the prepared pan and press it firmly and evenly into the bottom using your fingertips or the bottom of a measuring cup. Bake for 15–18 minutes, until just turning light golden around the edges and set but not deeply browned.
While the crust bakes, whisk the 4 eggs and 1 1/2 cups granulated sugar together in a large bowl until well combined and slightly pale. Add 1/3 cup flour and 1/4 teaspoon fine sea salt, whisking until smooth and no dry streaks remain.
4 large eggs, 1 1/2 cups granulated sugar, 1/3 cup all-purpose flour, 1/4 teaspoon fine sea salt
Pour in the fresh lime juice, lime zest, coconut milk, and 1 teaspoon vanilla. Whisk until the mixture looks silky and well blended. Stir in 1/2 cup unsweetened shredded coconut. The batter will be thin, with coconut flecks throughout.
1/2 cup fresh lime juice, 2 tablespoons finely grated lime zest, 1/2 cup canned coconut milk, 1 teaspoon pure vanilla extract, 1/2 cup unsweetened shredded coconut
When the crust is done, carefully pour the lime coconut filling evenly over the hot crust. Return the pan to the oven and bake for 22–28 minutes, or until the center is set and no longer jiggly when you gently shake the pan. The top may have tiny bubbles or a very light golden color at the edges.
Remove the pan from the oven and place it on a wire rack. Let the bars cool completely to room temperature, then cover and refrigerate for at least 2 hours, or until fully chilled and set for clean slices.
Use the parchment overhang to lift the chilled slab from the pan onto a cutting board. Dust the top with powdered sugar and add extra lime zest or thin lime slices and toasted coconut, if desired. Use a sharp knife, wiping the blade with a warm, damp cloth between cuts, to slice into 24–30 bars.
powdered sugar, extra lime zest or thin lime slices, toasted shredded coconut