Combine sugar, grated chocolate, milk, and butter in a large Dutch oven; cook over medium heat, stirring constantly, until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, stirring occasionally, until mixture reaches soft ball stage (234°).
Remove from heat; let stand 15 minutes or until mixture cools to lukewarm (110°). Do not stir. Add vanilla and coconut; beat mixture with a wooden spoon until mixture thickens and begins to lose its gloss.
Working rapidly, spread mixture into a buttered 9-inch square baking pan. Mark top of warm candy into 1 1/2-inch squares, using a sharp knife. Cool completely before cutting into squares. Store in an airtight container.