Cream the butter and sugar using an electric mixer over medium speed until the mixture is smooth and fluffy. Add in the whisked egg, half at a time, and beat over low speed. Add in the vanilla extract; mix well.
Sift in the flour in two batches and mix until well combined. Knead into soft dough.
Roll out the dough to a 1/2-cm thickness. Cut the dough with a cookie cutter (a bit smaller than a tart tin). Line the dough in the middle of tart tins. Lightly press the dough with your thumbs, starting from the bottom then up to the sides, turning and pressing to make an even tart shell. Trim the excess dough.
Prepare the Custard. Mix the sugar into hot water until dissolved. Whisk the egg with evaporated milk, cream, and vanilla. Pour in the sugar water and mix well. Sift the egg mixture and carefully pour into each tart shell.
Preheat the oven to 200°C (400°F). Bake the tarts in the lower level of the oven for 10 to 15 minutes or until the edges are lightly brown.
Lower the heat to 190°C (375°F). Keep an eye on the tarts. Once the custard puffs up a bit, pull the oven door open, about 2 to 3 inches. Bake for another 10 to 15 minutes until the custard is cooked through. Insert a toothpick into the custard. If it stands on its own, it's done.