Preheat the oven to 400°F/200°C, fan oven 180°C. Lightly grease a 9-inch pie dish.
Roll out the pie crust and fit it into the pie dish. Trim any excess dough and crimp the edges.
Place parchment paper in the middle of the pie dish and fill with dried beans or pie weights and make sure the weights are evenly distributed around the pie crust. Bake for 15 minutes in the preheated oven. Then remove the pie weights, foil, and parchment paper, and dock the pie with a fork, then bake for 10 more minutes. Remove from the oven and set aside to cool. Turn the oven down to 350°F/180°C, 160°C fan oven.
To a saucepan, add about an inch of water and sliced carrots and cook for 15 minutes or until soft. Drain well and allow to cool for 10 minutes.
Place the cooked carrots in a food processor and blend for 1 minute. Then add granulated sugar, brown sugar, milk, eggs, vanilla extract, ground cinnamon, ground nutmeg, ground ginger, and salt. Blend until the carrots are completely smooth and the mixture is well blended.
Pour the carrot mixture into the prepared pie crust, spreading it out evenly.
Place the pie dish on a baking sheet to catch any drips, and then transfer it to the preheated oven.
Bake for about 50-60 minutes, or until the filling is set and the crust is golden brown.
Remove the pie from the oven and let it cool completely on a wire rack. This will allow the filling to set further. Transfer to the fridge, and chill for at least 2 hours before serving.
Once cooled, you can optionally serve the carrot pie with a dollop of whipped cream or a scoop of vanilla ice cream.