Heat oven to 350ºF. Line an 8-inch square pan or baking dish with parchment. I like to cut a long parchment strip to fit inside the edges of the pan and let it hang over two sides. That way I can pull the bars out to cut them.
In a food processor blend the graham crackers until they are very fine crumbs. Add the toasted coconut, sugar and butter and pulse until mixture resembles wet sand. Press the crust mixture evenly onto bottom of the prepared pan. Bake until dry and lightly brown, about 10 minutes. Let cool on a wire rack. (Leave oven on)
Make filling: Mix egg yolks in the bowl of an electric mixer fitted with the whisk attachment on high speed until very thick, about 5 minutes. Reduce speed to medium. Add condensed milk in a slow, steady stream, mixing constantly. Raise speed to high; mix until thick, about 3 minutes. Reduce speed to low. Add lime juice; mix until just combined.
Spread filling evenly over crust using a spatula. Bake, rotating dish halfway through, until filling is just set, about 10 minutes. Let cool completely on a wire rack. Refrigerate at least 4 hours (or overnight).
For topping: Put cream and confectioners' sugar in the clean bowl of an electric mixer fitted with the whisk attachment. Mix on medium-high speed until stiff peaks form.
Remove bars from pan using overhanging parchment and cut into squares. Garnish bars with whipped cream, a slice of lime and toasted coconut.
Swap Key limes for regular or Persian limes in this recipe.