Combine sugar, grated chocolate, and milk 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 (236°).
Remove from heat; add butter and vanilla (do not stir). Let stand 15 minutes or until mixture cools to lukewarm (110°). Beat with a wooden spoon until mixture thickens and begins to lose its gloss.
Working rapidly, spread mixture in 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. Store in an airtight container.