Preheat the oven to 375 degrees F. Spray a 12-cup muffin tin with nonstick cooking spray.
Cut the pie crust into 12 pieces and press them evenly into the bottoms and up the sides of the muffin cups to form a crust.
In a medium bowl with an electric hand mixer, beat together the butter and sugar until fluffy. Add the eggs, pumpkin pie spice, and vanilla and mix well. Stir in the raisins and walnuts. Spoon the mixture evenly into the crusts.
Put the muffin tin onto a baking sheet and bake until the filling is set, 18 to 20 minutes. Remove the pan from the oven and allow to cool for 10 minutes. Carefully unmold the tarts, put them onto a rack, and let them cool to room temperature.