Special equipment: one 9-inch nonstick tart pan or one 9-inch springform pan
For the lime shortbread crust: Position an oven rack in the top third of the oven. Preheat the oven to 375 degrees F.
Add the flour, granulated sugar and salt to a food processor and pulse 2 to 3 times to combine. Add the cold butter cubes and pulse until the butter breaks down into small, uniform-size pieces, about the size of small pebbles. Add the lime zest and egg yolks and process a few more seconds or until the mixture looks like wet sand; the dough will not come together into a ball.
Spray a 9-inch nonstick tart pan lightly with cooking spray, making sure to spray the sides of the pan as well as the bottom. Pour the dough into the tart pan and spread evenly. Using your hands, press the dough into the bottom and up the sides of the pan. To prevent any dough from falling out of the pan, place your left thumb over the top of the pan along the crust and press the dough up the sides with your right pointer finger. This way, you will tightly pack the dough along the sides with your pointer finger and stop it at the top of the pan with your left thumb. Continue to press the dough into the pan and along the sides until it is tightly packed and evenly distributed. Poke the bottom of the crust with a fork all over and then place the tart pan on a baking sheet.
Bake until the sides of the crust are a deep golden brown and the crust bottom is light golden brown on top, about 25 minutes. Let cool completely.
For the mango filling: Add the mango and lime juice to a blender and puree on high speed for 1 minute until completely smooth. Hold in the blender.
In a small bowl, mix together the gelatin and 1/2 cup of the coconut milk. Let stand 5 minutes. As the gelatin rehydrates, the coconut milk will begin to look curdled; don't worry--it isn't.
Set a medium saucepan over medium heat and add the granulated sugar, salt and remaining coconut milk (about 1 1/4 cups). Stir the mixture together and bring to a simmer. Continue to simmer until the sugar melts completely; the coconut milk will become opaque. Remove from the heat and immediately whisk in the gelatin mixture. until completely melted. Strain the mango mixture into the coconut milk mixture and whisk again to combine. Let the mixture cool to room temperature, about 20 minutes.
Using a hand mixer, whip the heavy cream until soft peaks form. Fold the whipped cream into the mango filling and then pour the entire filling into the cooled tart crust; the filling will come to the very top of the crust. Refrigerate for 2 hours to set the filling completely. You can make the tart up to this point 1 day in advance.
For the tequila-lime glaze: Line a baking sheet with a cooling rack. Cut the 2 larger sides of the mango off of the pit, followed by the 2 smaller sides. Peel the 4 pieces of mango, then cut them into 1/4-inch half-moon slices.
In a small bowl, whisk together the confectioner' sugar, tequila and lime juice. Dip each slice of mango into the glaze and coat completely. Let drip dry over the bowl for a few seconds, then lay the mango pieces on the cooling rack for at least 15 minutes for the glaze to set.
When ready to serve, remove the tart from the tart pan and place on a cake stand. Lay the mango slices in a circle around the tart, setting aside the smallest slice for later; the mango slices will meet in the center of the tart and then fan out overlapping each other around the tart. Roll the reserved mango slice into a rosette and place in the center of the tart. Garnish with the lime zest and serve immediately.
You can use a knife or vegetable peeler to remove the peel from a mango, but I find the easiest way to remove it is to find a large glass with a thin rim. Place the mango in the palm of your hand so that the flesh of the mango is facing out. Line the top of the mango up with the rim of the glass. Gently press the mango against the glass so that the peel goes on the outside and the mango meat goes on the inside. Continue to guide the mango with your palm along the rim of the glass so that the peel separates completely and the mango falls into the inside of the glass. A fresh, ripe mango is best for this dish, but you can substitute frozen cubed mango in the same amount for the tart filling. Fresh lime juice is a much better, more flavorful product to use then shelf-stable lime juice. You can squeeze lime juice in advance, place in an airtight, freezer-safe container and hold in the freezer. Defrost the lime juice the night before you want to use it. It is better not to heat the lime juice in any way when defrosting, as it might change the flavor.