FOR THE COOKIES: Whisk flour, cocoa, salt, baking powder, and baking soda together in bowl; set aside. Using stand mixer fitted with paddle, beat oil and sugar on medium-high speed until fluffy, about 2 minutes. Reduce speed to low; add milk, egg, and vanilla; and beat until combined, about 30 seconds. Slowly add flour mixture and beat until just combined, about 1 minute, scraping down bowl as needed. Divide dough in half. Form each half into 4-inch disk, wrap disks tightly in plastic wrap, and refrigerate until dough is firm yet malleable, about 45 minutes.

Adjust oven racks to upper-middle and lower-middle positions and heat oven to 350 degrees. Line 2 baking sheets with parchment paper. Working with 1 disk of dough at a time, roll into 11-inch circle, about ⅛ inch thick, between 2 large sheets of lightly floured parchment paper. Remove top piece of parchment. Using 1¾-inch round cookie cutter, cut dough into rounds; space rounds ½ inch apart on prepared sheets. Gently reroll scraps ⅛ inch thick, cut into rounds, and transfer to prepared sheets. Bake until cookies are very firm, 16 to 18 minutes, switching and rotating sheets halfway through baking. Let cookies cool on sheets for 5 minutes, then transfer to wire rack. Let cookies cool completely.

FOR THE CHOCOLATE COATING: Line baking sheet with parchment paper. Microwave finely chopped chocolate and oil in bowl at 50 percent power, stirring often, until about two-thirds melted, 2 to 4 minutes. (Melted chocolate should not be much warmer than body temperature; check by holding bowl in palm of your hand.) Add grated chocolate and stir until smooth, returning to microwave for no more than 5 seconds at a time to finish melting if necessary.

Working with 1 cookie at a time, place cookie on fork and dip bottom of cookie in chocolate. Using offset spatula, spread chocolate over top of cookie, creating thin coating. Transfer cookie to prepared baking sheet and repeat with remaining cookies. Let cookies sit until chocolate sets, about 15 minutes, before serving. (Cookies can be stored at room temperature for up to 2 weeks.)