Preheat the oven to 350°. Sift the flour and toss with the coconut flakes.
In the bowl of a stand mixer, combine the almond butter, butter, brown sugar, white sugar, baking powder, baking soda, salt, vanilla and almond extracts. Mix on low speed to moisten, then increase to medium and beat one minute.
Add the egg and continue creaming until smooth, pausing to scrape the bowl and beater with a flexible spatula as needed. Reduce speed to low, add the coconut/flour, and continue mixing until the dry bits disappear.
Use a large cookie scoop (2 1/2 Tablespoons) to portion the thick dough into 18 pieces. Roll each one smooth and round, and arrange on two baking sheets. For thick and chewy cookies, leave the dough-balls alone. For thin and crispy cookies, flatten with a drinking glass. You can see the hodge-podge of thicknesses below.
If you like, sprinkle the dough with an extra pinch of salt. Bake until the cookies are puffed and firm around the edges, though their centers will still seem a little steamy and damp; about 15 minutes.
While the cookies cool, gently melt the chocolate (if you melt it over a water bath and keep the chocolate below 95°, it will stay in good temper). Transfer to a small parchment cone, snip the end and drizzle the cookies with melted chocolate.
The cookies will keep for a few days in an airtight container, with a sheet of wax paper between the layers.