★For Tart Dough
Crush lumps of maple sugar beforehand. Cream unsalted butter until smooth. Add the maple sugar in 3 parts, and mix well each time.
Use an electric mixer to beat on low speed for 2 mins until whitish.

Add beaten egg (room temperature) in 3 parts, and beat well each time. Add vanilla oil and mix well. Sift cake flour over, and use a spatula to fold it until large clumps.

Gather the dough in the center. Use a spatula to press and spread the dough to stick it to the inside of the bowl. Repeat it two more times. Wrap it with plastic wrap and flatten it. Let it sit in a fridge for 3 hours to overnight.

★For Almond Cream
Cream unsalted butter until smooth. Add granulated sugar in 2 parts, and mix well each time. Use an electric mixer to beat on low speed for 1 minute.

Warm beaten egg with hot water until 35℃ / 95F, about body temperature. Add the egg to the butter mixture in 6 parts. Beat it on low speed until smooth thoroughly each time.

Sift ground almonds and flour over the mixture. Use a spatula to mix until smooth. Transfer it to a small bowl, and seal it with plastic wrap. Let it sit in a fridge for 3 hours to overnight.

★Bake blind
Preheat an oven to 190℃ / 374F. Take out the tart dough, leave it for 5-10 mins, and press it to soften.
Flour it, and use your hands or rolling pin to shape it roughly to a round shape. Put it in a tart pan.

Cover it with plastic wrap. Use a cup to press the dough into the bottom and side into 3 - 5 mm / 0.1 - 0.2 inches thick. Trim away any excess. Chill in a fridge for 15-30 minutes. Prick the base with a fork.

Line it with parchment paper and fill the inside with tart stones. Lower the oven to 170 ℃ / 338 F, and bake for 15-18 minutes until the edges are slightly brown.
Remove the tart stones and the paper and bake for another 5 minutes until the bottom is dry. Let it cool.

★For Custard
Put egg yolks and granulated sugar in a small pot and use a whisk to stir until whitish a little. Add vanilla oil and mix, then sift cake flour over and stir until smooth.

Put milk and 1 tsp granulated sugar in a heat-resistant container, mix lightly, and heat in the microwave at 600W for 1 minute. (Sugar prevents scum from forming.)
Pour the warm milk into the egg mixture while stirring. Stir well until smooth.

With stirring, heat it over medium heat. When it starts to thicken and form lumps, turn off the heat and stir well until smooth.

With stirring, heat again over medium heat for 2 minutes. You should heat it until some big bubbles should come out when you stop stirring.

Put it out on a tray and cover it with plastic wrap, then put ice or ice packs on it to cool it quickly. Set aside.

★For Frangipane
Remove the almond cream from the fridge and let it soften at room temperature.
Transfer well-chilled custard, 70 g / 2.5 oz, to a bowl. Use a spatula to loosen until smooth. (A well-cooked custard will harden when cooled.) Add the softened almond cream and mix until smooth.

★For Bake
Preheat an oven to 190℃ / 374 F. Put the Frangipane into a well-cooled tart crust and flatten it. Lower the oven to 170 ℃ / 338 F, and bake for 35-40 minutes until golden brown.
Make syrup. Add granulated sugar to hot water and stir well to dissolve the sugar. Add kirsch, and stir. Let it cool for 5 minutes.

Brush gently the top of Frangipane with the syrup, with a little space on the edge. Cool completely and remove from the pan.

★For Diplomat Cream
Loosen the remaining custard until smooth.
Add granulated sugar to heavy cream. Whip it until thickened while cooling in ice water. Take it out from the ice water, add vanilla essence, and whip it until soft peaks form.
Add half of the whipped cream to the custard and fold gently. Let the remaining whipped cream in a fridge. Use it for decoration later.

For Assembling
Squeeze out the Diplomat Cream over the Frangipane, with a little space on the edge. Squeeze it so that the center rises like a gently sloping hill.
Use a knife to peel off mangoes. Cut cheeks from the stone, and slice each into 5mm / 0.2 inches thick.
Arrange the mango slices on the top, starting in outwards to the center. Pipe the remaining whipped cream along the edges.
It's all done. It tastes better when chilled.