Combine Brown Sugar (1/2 cup), Salt (3 tablespoon), Ground Black Pepper (2 tablespoon), Smoked Paprika (1 tablespoon), Granulated Garlic (1 teaspoon), Spanish Smoked Sweet Paprika (1 teaspoon), Dry Mustard (1 teaspoon), Chipotle Chili Powder (1/2 teaspoon) and Cayenne Pepper (1/2 teaspoon) in a small bowl, stir, and pour into a shaker or seasoning dredge.
Apply generous coat of dry rub mixture to all sides of Beef Short Ribs (3 pound) and pat gently.
Prepare Big Green Egg for direct grilling at 350-400 degrees F (176-204 degrees C) using Lump charcoal and pecan wood chunks for smoke flavor. Any type of grill can be used for this recipe.
Arrange short rib pieces on cooking grate and cook for 35-40 minutes turning often. Short Rib pieces should be well browned on all sides. Cook until the outside is caramelized moving around the cooking surface as needed.
Serve family style with your favorite sides and pickled items.