Cream the butter and sugar together until they are light and fluffy. Add the egg and mix until just incorporated.
Add the flour and mix until a soft dough is formed. Use your hands if needed to form the mixture into a dough.
Form the dough into a ball and place in saran wrap in the freezer for 10-15 minutes.
Once chilled, roll the dough out and place into your tart pan. Place in freezer for another 10-15 minutes.
Use a fork to prick the bottom of the crust and place into a 400 degree oven for 16-18 minutes, until golden brown. Remove and let cool completely. If you're not assembling the tart the same day, the crust can be stored covered on the countertop for several days.
To Make Coconut Cream:
Mix the sugar and egg yolks together in a heat-proof bowl.
Then add the flour and cornstarch and mix until incorporated.
In a separate saucepan, heat the coconut milk until its uniformly warm. Remove from heat and pour slowly into the egg yolk mixture while stirring constantly.
Once everything is mixed well, pour back into the saucepan. Heat again over medium heat, stirring constantly for another minute or two until the pastry cream becomes thicker.
Remove from heat, pour into a bowl, and cover with saran wrap. The pastry cream can be saved in the refrigerator for several days. If it becomes too thick while resting, add additional coconut milk to thin it out.
To Make Sweet and Salty Coconut Sauce:
Mix the coconut milk, salt, and sugar over medium heat until the sugar and salt are dissolved and the mixture is smooth. This sauce can also be saved in the refrigerator for several days until you are ready to assemble and serve the tart.
To Assemble Tart:
Spread the cooled coconut cream into the pastry crust.
Peel a mango, and slice its two halves from the central seed. Lay the halves flat on a cutting board and make diagonal slices, just as you would if you were making Mango Sticky Rice. Then, go back and add one or two additional slices in between the diagonal cuts to achieve thinner slices. Repeat for all 4 mangoes.
Curl one mango slice in the middle of the cream-filled tart, then add additional mango slices around it until the tart is covered in a rose-shaped pattern.
Serve with a small bowl of the sweet and salty coconut sauce for your diners to drizzle onto their piece of mango tart before eating. Enjoy!
Notes
The best mangoes to use for this dessert are the Manila or Ataulfo (champagne) mangoes. If you're not able to find these, any variety that is ripe and sweet will work.