Adjust the oven rack to the middle position and heat oven to 350 degrees. Line a rimmed cookie sheet with parchment paper and spread pecans in an even layer, toast for 4 minutes, rotate pan, and continue to toast until fragrant and the color deepens slightly, about 4 minutes longer. Transfer the cookie sheet with the nuts to a wire rack.
For the spice nuts: While the nuts are toasting, stir together the sugar, salt, cinnamon, cloves and allspice in medium bowl; set aside. For the glaze: Bring the rum, vanilla, brown sugar and butter to a boil in medium saucepan over medium high heat, whisking constantly. Stir in the toasted pecans and cook, stirring constantly with a wooden spoon until the nuts are shiny and almost all liquid has evaporated, about one and one-half minutes.
Transfer the glazed pecans to bowl with spice mix; toss well to coat. Return the glazed and spiced pecans to parchment-lined cookie sheet to cool. The nuts can be stored in an airtight container for up to 5 days.