In a 2-3 quart pan, melt butter. Add brown sugar and salt to melted butter and stir to combine. Add in corn syrup. Gradually add condensed milk, stirring constantly over medium heat to a firm ball (225-230 degrees) on a candy thermometer. Remove from heat, add vanilla. Pour into a heavily buttered 9x13 pan. Sprinkle caramels lightly with kosher salt. Allow caramels to cool; cut with a pizza cutter and wrap caramels in wax paper.