Combine sugar, milk, and grated chocolate 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; add butter and vanilla (do not stir). Cool to lukewarm (110°). Beat until mixture thickens and begins to lose its gloss. Working rapidly, spread mixture in a buttered 9- inch square baking pan. Cut candy into 1-inch squares. Store in airtight containers.