Combine the polenta, flour, and sugar in a bowl, then cut in the cold butter until it looks like coarse crumbs. Add the egg yolk and mix gently until a dough forms. Wrap it in plastic and chill for about 20 minutes so it firms up.
Divide the chilled dough among your tins and press it evenly across the base and up the sides. Prick the bottoms lightly with a fork to stop them from puffing up. Pop the lined tins back in the fridge for 10 minutes.
Bake the crusts at 180°C (350°F) for about 12 minutes until just set and lightly golden. This short pre-bake keeps the base from turning soggy once the filling goes in. Let them cool slightly on the tray before filling.
Whisk together the eggs, sugar, cornstarch, mandarin zest, and juice until smooth. Slowly stream in the cream while whisking so nothing curdles. Stir in the vanilla and a pinch of salt to finish the mixture.
Pour the filling evenly into the pre-baked crusts, filling each about three-quarters full. Bake for 18 to 20 minutes until the centers are just set but still have a gentle wobble. Overbaking here will dry out the creamy texture you're after.
Let the tartelettes cool to room temperature, then refrigerate for at least an hour. This chilling step is what gives the filling its silky, sliceable texture. Serve them cold or just slightly chilled for the best flavor.