Preheat your oven to 300°F (150°C).
In a bowl, mix together brown sugar, salt, black pepper, and smoked paprika. Rub the mixture all over the pork shoulder.
Place the pork in a roasting pan and cover with aluminum foil. Cook for about 1 hour and 30 minutes, or until the pork is tender and shreds easily.
While the pork is cooking, heat olive oil in a large skillet over medium heat. Sauté the onion, garlic, and red bell pepper until softened.
Add the diced tomatoes, cumin, and chili powder to the skillet. Season with salt and pepper, and let simmer for 10 minutes.
Shred the cooked pork using two forks and stir in BBQ sauce. Add the pulled pork to the skillet with the tomato mixture and mix well.
Create wells in the pork and tomato mixture and crack an egg into each well. Cover the skillet and cook until the eggs are done to your liking.
For the cornbread crumble, in a bowl, mix cornmeal, flour, baking powder, and salt. Stir in milk, melted butter, and honey until just combined.
Crumble the cornbread mixture over the shakshuka and broil for 3-5 minutes until the topping is golden and crispy.
Serve the BBQ Pulled Pork Shakshuka with Cornbread Crumble hot.