For the pulled pork: Heat an electric pressure cooker on the saute mode. When hot, add the olive oil. Add half of the pork along with 1 tablespoon of the salt, 1 teaspoon of the chili powder, 1/2 teaspoon of the garlic powder and 1/2 teaspoon of the onion powder. Saute until the meat a little browned, about 10 minutes. Set the meat aside on a plate. Add the remaining meat, salt, and chili powder, garlic powder and onion powder and cook until the meat browned, another 10 minutes.
Add the first half of the meat back to the pressure cooker. Add the garlic and onions and cook, stirring, for 2 minutes. Pour in the chicken stock. Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on manual for 40 minutes.
After the pressure-cook cycle is complete, follow the manufacturer's guide for natural release. After 15 minutes, release the rest of the steam using quick release.
Remove the lid from the pressure cooker. Remove the pork and onions to a baking sheet. Shred the pork with 2 forks, pour the barbecue sauce over the top and toss to coat. Serve.
If not serving right away, transfer to a 9-by-13-inch disposable aluminum pan, cover with foil and keep warm in the oven at 300 degrees F until ready to serve.
For the Brussels sprouts: Preheat the oven to 375 degrees F. Trim/clean the Brussels sprouts, then cut them in half. Arrange on 2 baking sheets and toss with the olive oil and some salt and pepper. Roast until brown, about 35 minutes.
For the cheese grits: Bring the chicken stock to a boil in a saucepan. Slowly stir in the grits. Return to a boil and cook for 3 to 4 minutes. Turn down the heat and stir in the pepper jack, Cheddar, mascarpone, heavy cream and butter. Season with the salt. Cook for another 3 to 4 minutes. Keep warm until ready to serve.
To serve, spoon some grits onto a plate then top with pork and sprinkle with the Brussels sprouts.