Pour cream and milk into a heavy bottomed sauce pot. Set over medium heat and bring to a simmer. Stir occasionally to make sure milk does not burn along the sides or bottom of pot.
Meanwhile, whisk together sugar and cornstarch. Add egg yolks. Whisk until well combined. Add a few tablespoons of warming cream-milk to loosen mixture and whisk until smooth.
Once the cream-milk is simmering, reduce heat to low. Slowly add about 1/4 cup of the hot liquid into the egg mixture. Whisk constantly to distribute heat. Continue to temper the egg mixture by continuing to add 1/4 cup of hot liquid at a time until only a few tablespoons of liquid remain in the pot.
Pour all the egg-milk mixture back into the sauce pot. Use a spatula to stir mixture together. Continue to heat over low heat until mixture has reached temperature of 170° to 180°F (77° to 82°C) and has thickened to nappe (meaning when a finger is run across the back of the spatula, it leaves a well-defined track).
Remove from heat and stir in vanilla. Immediately pour mixture through a strainer. Let cool slightly, about 5 minutes. Then, pour into baked tart shells.
Place assembled tarts in the fridge uncovered for at least 3 hours until completely cooled and filling has set.