In a heavy-bottomed saucepan, bring brown sugar and cream to a boil over medium heat, stirring frequently until sugar dissolves. Cook, stirring constantly, until thick and a candy thermometer registers 230°F (110°C) to 235°F (113°C), 3 to 4 minutes. Remove from heat; stir in pecans, butter, salt, and vanilla. Let cool completely. Refrigerate in an airtight container for up to 2 weeks.