Prepare the Crust. Preheat oven to 350°F. Line a 9x13 inch baking dish with parchment paper, leaving a 2-inch overhang on the sides for easy removal later. In a food processor, pulse graham crackers, toasted coconut, sugar, and salt into fine crumbs. Pour in melted butter and pulse until the mixture looks like wet sand. Press firmly into the bottom of the prepared pan and bake for 8-10 minutes. Set aside to cool slightly.
Make the Filling. Reduce oven temperature to 325°F. In a large bowl or stand mixer, beat the softened cream cheese on medium-high until completely smooth (1-2 minutes). In a small separate bowl, whisk together the sugar and flour, then add to the cream cheese and mix until combined.
Add Liquids. Add the eggs and yolk one at a time, mixing gently after each. Add sour cream, lime juice, lime zest, and vanilla. Mix on low just until blended. Do not overmix.
Bake. Pour batter over the crust. Bake at 325°F for 30-35 minutes. The bars are done when the edges are set but the center still jiggles slightly like gelatin.
Chill and Serve. Cool on a wire rack at room temperature for 1 hour, then refrigerate for at least 4 hours. Use the parchment paper to lift the bars out of the pan before slicing.