Combine sugar, salt, and whipping cream in a 4-quart 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, and add butter (do not stir). Let stand 15 minutes or until mixture cools to lukewarm (110°). Add vanilla and pecans; beat mixture with a wooden spoon until mixture thickens and begins to lose its gloss.
Working rapidly, drop mixture by tablespoonfuls onto buttered waxed paper. Cool completely. Remove from waxed paper, and store in airtight containers.