In the bowl of an electric mixer fitted with the paddle attachment, beat 8 tablespoons butter and the sugar on medium speed until fluffy. Add the egg and vanilla, and beat until combined.
In a medium bowl, whisk flour, baking soda, and salt. Add flour mixture to butter mixture, and beat on low speed until combined. Add coconut, and beat until combined. Roll out the dough between two 12-by-17-inch pieces of parchment paper into a 10 1/2-by-15 1/2-inch rectangle, a scant 1/4 inch thick. Using a sharp knife, trim to even dough to a 10-by-15-inch
rectangle. Transfer dough to a baking sheet, and place in refrigerator to chill at least 1 hour.
Place the chocolate and the remaining tablespoon butter in the top of a double boiler or a heat-proof bowl set over a pan of simmering water. Melt completely, about 2 minutes, and remove from heat. Stir in the condensed milk. Let stand until slightly thickened, about 5 minutes.
Remove the dough from the refrigerator. Peel off the top piece of parchment. Using an offset spatula, spread the melted chocolate mixture over the dough.
Using the bottom piece of parchment for support, roll the dough into a log. Wrap the log in parchment, and chill overnight.
Preheat oven to 350 degrees. Have ready two baking sheets lined with parchment paper. Remove the parchment from the log, and cut log into 1/4-inch-thick rounds. Place the rounds on the baking sheets, spaced 1 inches apart. Bake until light golden brown on edges, 8 to 10 minutes, rotating halfway through. Transfer cookies to a wire rack to cool. Bake or freeze remaining dough. Store the cookies in an airtight container up to 2 weeks.