For the Coconut-Infused Milk: Toast the coconut in a 176°C / 350°F oven until it begins to have a toasted aroma. Bring the skim milk to a simmer over medium-high heat. Steep toasted coconut while it is hot in the hot skim milk. Strain through a fine-mesh strainer.
For the Ice Cream Base: Make the ice cream base according to the Classic Ice Cream Method.
Add the coconut purée once the custard is made and hot. Whisk thoroughly to completely dissolve the coconut purée.
Strain the base through a fine-mesh strainer and cool over an ice bath. Age the base under refrigeration overnight.
Once the base has aged, churn to the desired consistency.
Harden for at least 2 hours and up to 4 hours. Reserve until needed.