Bake pie crust according to package instructions, being sure to weight the crust using aluminum foil and beans to keep the crust from shrinking. Allow to cool completely and set aside.
Preheat oven to 350 degrees.
Place carrots in a large pot and cover with water. Bring water to a boil, then reduce heat. Simmer for 30 minutes, until carrots are fork tender.
Drain the water from the carrots and place them back in the pot. Cook over low heat for two minutes, stirring constantly, to remove excess water from the carrots.
Place carrots and butter in the bowl of a food processor. Pulse until carrots are smooth.
Pour pureed carrots into a large bowl. Add sugar, brown sugar, and eggs. Stir to combine.
Season with cinnamon and pumpkin pie spice, then add vanilla, milk and flour. Stir to combine.
Pour mixture into baked pie crust. Bake in preheated oven for 50 to 60 minutes or when a toothpick inserted into the center of the pie comes out clean.
Place cooked pie on a wire rack to cool for two hours, then refrigerate for one to two hours before serving.