1Preheat oven to 325 degrees with racks in upper and lower thirds. Line two baking sheets with parchment paper.
2Put 7 oz. (2 2/3 cups) flaked coconut and the powdered sugar in a food processor and whirl 30 seconds. Add remaining ingredients except chocolate. Whirl until coconut is well chopped, scraping down the sides inside the processor once.
3Pour remaining 5 ounces (1 3/4 cups) flaked coconut into a medium bowl. Drop a generous tablespoon of dough into the bowl and gently toss to coat with coconut. Roll into a ball between your palms, then roll in coconut again and set on baking sheet. Repeat until all dough is used, setting cookies about 1/2 inch apart (they don't spread much).
4Bake until golden around the top and edges, switching position of pans halfway through, 25-30 minutes total. Slide parchment with cookies onto a rack and cool completely.
5Melt chocolate in microwave taking care not to burn it. It should be the consistency of sour cream.
6Line a baking sheet with waxed paper. Hold one cookie at a time by the top and dip the bottom into chocolate about 1/2 inches up the side of cookie. Set on baking sheet and chill 1 hour to set the chocolate.