Preheat oven to 400 degrees F (200 degrees C). Place tart shells on a baking sheet.
Whisk brown sugar, butter, and vanilla extract together in a bowl; whisk in egg until smooth. Stir half-and-half into sugar mixture. Fill prepared tart shells 2/3-full with filling.
Bake in the preheated oven until filling is bubbly and pastry is golden, about 15 minutes.
