In a medium bowl, whisk together flour, baking powder, baking soda, 1/2 tsp. salt, and nutmeg.
In the bowl of a stand mixer fitted with the paddle attachment, beat together sugar, butter, 2 tsp. coconut extract, 1 tsp. vanilla extract, 1 cup of coconut milk, and egg until well-incorporated.
Gently add the dry ingredients to the bowl of the stand mixer and mix until a soft & sticky dough forms.
In a 5 1/2 quart dutch-oven, or similar, heat up 1 quart (4 cups) of canola oil to 370 °F (188 °C)
While the oil is heating up, using lightly oiled hands, roll 1/4 cup of dough into a loose ball and gently pat down on it forming a disc. Using your thumb, form a 1 1/2-inch hole in the center (or you can use a small biscuit cutter to cut out the center). Do this for the remaining dough.
Once the oil has heat up to the correct temperature, gently drop the donuts, 2-3 at a time, into the hot oil and fry until puffed and golden on both sides, about 3 minutes.
Using a slotted spoon or spider strainer, transfer donuts to a wire rack covered with two paper towel layers to cool completely. Repeat until all donuts have been fried.
While the donuts are cooling, make the topping.
Preheat the oven broiler and line a large baking sheet with parchment paper. Spread the shredded coconut on the baking sheet in an even layer and place under broiler. YOU NEED TO WATCH THIS CAREFULLY. Coconut toasts FAST under a broiler and you DO not want to burn it. As soon as you see the slightest hint of brown on your coconut, remove from oven. It continues to cook. If you take it out too late, your coconut may burn/turn black as it cools since it's still "cooking."
In a medium bowl, big enough for you to dip the donuts in, whisk together remaining salt, extracts, coconut milk, and confectioners' sugar until smooth.
Set up an assembly line for yourself. Donuts, glaze, toasted coconut. Take a cooled donut and dip one top half into the glaze, let the excess drain off then immediately dip it in the toasted coconut. Repeat until all donuts have been topped.
Store in an airtight container for no longer than 3 days.
Notes
You'll want to keep your oil temperature steady at 370 degrees Fahrenheit. Using a candy/frying thermometer is the most handy in this situation because it just clips to the side of your pot.If you notice your oil getting too hot, cut the heat. If you notice it cooling down rapidly, turn up the heat or fry less donuts at the same time.Source: Saveur