Preheat oven to 325° with racks in upper and lower thirds. Line 2 baking sheets with parchment paper.
Put 7 oz. (2 2/3 cups) flaked coconut and the powdered sugar in a food processor and whirl 30 seconds. Add all remaining ingredients except chocolate. Whirl until coconut is well chopped, scraping down inside of processor once.
Pour remaining 5 oz. (1 3/4 cups) flaked coconut into a medium bowl. Drop a generous tablespoonful of dough into 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 with remaining dough and flaked coconut, setting cookies about 1/2 in. apart (they don't spread much).
Bake until golden around the top and edges, switching position of pans halfway through, 25 to 30 minutes total. Slide parchment with cookies onto a cooling rack to cool completely.
Break or chop chocolate into small chunks, put in a small microwave-safe bowl, and heat in 20-second bursts until almost melted. Stir to melt completely. If very liquidy, let cool until as thick as sour cream.
Line a baking sheet with waxed paper or parchment. Hold one cookie at a time by the top and dip the bottom into chocolate about 1/2 in. up the side of cookie. Set on baking sheet and chill 1 hour to set chocolate.
*Find cream of coconut and coconut flour at well-stocked grocery stores.
Make ahead: Up to 2 weeks, chilled airtight.