Remove the stems from each chili, and remove the seeds if desired. (It's generally a good idea.)
Add the chilis to a heat resistant mixing bowl, then pour 2 cups boiling water over it. Let steep for 20 to 30 minutes, or until the chilis have softened and are pliable.
Meanwhile, heat a large skillet over high and drizzle with the oil. Salt and pepper the pork chunks, then brown in the pan to just to form a crust. Transfer the seared meat to the slow cooker.
Add the diced onion, garlic, hominy, broth, oregano, cumin, and paprika to the slow cooker.
Once the peppers have finished steeping, transfer them to a blender along with 1 1/2 cups of the water they rested in. Blend to form a smooth purée. Add the chili paste to the slow cooker (strain if desired). This chili purée is what makes it a red pozole, as opposed to white or green.
Cover and cook on low for 8 hours, or on high for 4 hours. Just before serving, squeeze a lime into it. Serve with a side of limes as well as your favorite garnishes, such as radishes, cilantro, red onion, and even cabbage.