Bring 1 1/2 cups sugar, the milk, and salt to a boil in a small saucepan, stirring until sugar dissolves. Remove from heat (mixture may look separated).
Bring water and remaining 3/4 cup sugar to a boil in a medium saucepan over medium-high heat. Wash sides of pan with a wet pastry brush to prevent sugar crystals from forming. Cook, undisturbed, until sugar begins to turn light gold, about 5 minutes. Swirl pan, then cook until caramel turns amber, about 2 minutes. Immediately remove pan from heat. Carefully stir in milk mixture (liquid may bubble up), then pecans. Place pan over medium heat, and cook, stirring often, until caramel registers 242 degrees on a candy thermometer, about 7 minutes.
Remove pan from heat, and stir in butter, vanilla, and rum. Continue stirring until caramel cools and becomes very thick and difficult to stir, about 10 minutes. Drop small mounds of caramel onto a baking sheet lined with a nonstick baking mat, and let cool.
Place melted chocolate in a medium bowl. Using an offset spatula, dip bottom of each pecan cluster into chocolate, leaving top partially undipped. Place dipped pecan clusters on a parchment-lined baking sheet, and let stand until chocolate is set. Pecan clusters will keep, covered, for up to 5 days.
Get the packaging how-to for the Pecan Clusters.