Preheat the oven to 400°F. Line two baking sheets with parchment paper.
Place the flour, baking powder, sugar, and salt in the bowl of an electric mixer and mix on low speed for a few seconds to combine. Add the butter and mix on low speed for 3 to 4 minutes, until the butter is the size of peas. Gradually add the cream and mix until the dough comes together.
Divide the dough in half and knead each half on a lightly floured work surface to bring the dough together completely. Pat each piece of dough to a ¾-inch thickness. Using a 2-inch round biscuit cutter, cut out circles of dough and place on the prepared baking sheets, spacing them 2-inches apart. Brush the tops of the biscuits with the egg wash. Bake for about 20 minutes, until golden brown and firm to the touch. Remove from the oven and let cool completely on the pans.
Reduce the oven temperature to 225°F. Combine the sugars, salt, paprika, chili powder, cumin, and black pepper in a small bowl. Sprinkle the rub all over the pork and gently pat it down so that it sticks to the meat. Place the pork on a wire rack set over a large rimmed baking sheet. Roast the pork for about 7½ hours, until the pork falls apart easily and registers 200°F on a meat thermometer. Transfer the pork to a large cutting board and shred the meat into bite-size pieces. Stir together the pulled pork and barbecue sauce in a large bowl.
To assemble, cut the biscuits in half crosswise. Spoon the pork over the bottom halves of the biscuits and place the top halves over the pork.