1. In the bowl of a stand mixer fitted with beater attachment (or a large bowl), dissolve yeast in water and allow to sit for about 5 minutes until bubbly. Beat in coconut milk and sugar, and salt. Add about 2 cups flour, one cup at a time, until your dough comes together and pull away from the sides. Now switch the attachment to a dough hook and add up to 1/2 cup more flour as need until the dough is smooth and resilient. Cover bowl with a damp towel or plastic wrap and place in warm place to rise until doubled in size. (Alternatively, you can refrigerate the dough overnight.)
2. When dough is ready, roll it out on a lightly floured surface into a layer about 1/2 inch thick. Use a circular cookie cutter with a diameter of about 3 inches (or you can use the mouth of an inverted cup) to cut out circles. Place the doughnuts on a tray and allow them to rise for 30 to 45 minutes.
3. After they've been rising for close to 25 minutes, heat oil to 350 degrees F (180 C) in a deep fryer or wide pot and line a plate with paper towels. Drop doughnuts, a few at a time, gently into oil and fry on each side for about 1 minute or until golden brown. Remove with a slotted spoon and place on prepared plate.

Chocolate Glaze:

1. Whisk all the ingredients together in a medium mixing bowl until completely smooth. Pour it into a shallow dish and dip the tops of doughnuts one by one and place on a parchment lined tray to dry. 

Buttercream Filling:

1. Beat butter in a large mixing bowl fitted with whisk attachment until creamy. Add vanilla, salt, and powdered sugar one cup at a time. Add milk and beat until light and fluffy. Add a bit more milk or powdered sugar if needed for it to be a thick but pipe-able consistency.
2. Now fill a pastry bag fitted with a long narrow tip with the buttercream. Use a sharp skewer to poke holes into the sides of each doughnut then pipe the filling into holes to fill each one.
3. These are best served as soon as possible!