Preheat the oven to 400 degrees F (200 degrees C). Place tart shells on a baking sheet. Bake in the preheated oven for 1 minute. Remove from oven, leaving oven on. Combine pumpkin puree, evaporated milk, eggs, brown sugar, pumpkin pie spice, cinnamon, and vanilla extract in a large bowl. Whisk until well combined. Pour filling into tart shells. Bake in the preheated oven for 10 minutes. Turn pan and bake until set, about 12 minutes more. Cool tarts for 10 minutes; refrigerate until chilled, about 1 hour. Serve with whipped cream.