Combine the shortening, flour, salt, and baking powder in a food processor or a stand mixer fitted with a dough hook. Blend until the ingredients are fully combined and begin to clump. Slowly add in the water until a single dough ball forms. Cover and refrigerate the dough for 1–2 hours.
Prepare the grill for parallel two-zone grilling, spreading pre-heated Kingsford® briquets on the sides of the grill’s charcoal grate and leaving the center cool. Replace the main cooking grate, add 2–3 chunks of your favorite smoking wood to the charcoal, then adjust the bottom grill vents to bring the temperature to 350°F.
Season chicken thighs with barbecue dry rub seasoning then place on the cool portion of the grill, cover the grill, and allow the thighs to smoke until they reach an internal temperature of 165°F (approximately 45 minutes). Remove the thighs from the grill and set aside to cool before removing the meat from the bone and shredding.
Take the dough out of the refrigerator and roll it out to a thickness of approximately 1/8 inch. Cut the dough into circles using a 3½-inch ring mold or by hand with the tip of a paring knife. Add approximately 1 tbsp. of shredded smoked chicken to one half of each dough round then fold the other side over the chicken to create a half moon. Use a fork to crimp the edges of the half circle. Using a paring knife, make two small slits in the top of each pie (pasty) then use a pastry brush to coat the top with beaten egg.
Cover a sheet pan with parchment paper and set the pasties on the parchment. Place the sheet pan on the grill between the parallel lines of charcoal. Cover the grill and allow the pasties to cook for 20–30 minutes until the pastry is golden brown.
Remove and serve immediately with ranch dressing.