Toast the dried chiles in a large heavy-bottomed pot or Dutch oven over medium-high heat, turning often, until slightly darkened and fragrant, about 4 minutes. Remove to a plate and set aside. Heat 2 tablespoons olive oil in the pot. Add the Fresno chiles, red onion, garlic, cumin, oregano, 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring, until the onion softens, about 4 minutes. Add the tomato paste and cook, stirring, until the vegetables are coated, about 1 minute.
Add the tomatoes, beef broth, masa harina, brown sugar, vinegar and the toasted chiles to the pot. Bring to a boil, then reduce the heat to low; cover and simmer until the dried chiles soften, about 20 minutes. Working in small batches, puree the mixture in a blender and transfer to a large bowl. Wipe the pot clean.
Season the beef and pork generously with salt and pepper. Heat the remaining 2 tablespoons olive oil in the pot. Working in batches, add the meat in a single layer and cook, turning, until browned, about 7 minutes. Remove each batch to a bowl with a slotted spoon as you go.
Return the meat to the pot along with the pureed mixture and 3 cups water. Bring to a boil, then reduce the heat to low; partially cover and cook, stirring occasionally, until the meat is tender, about 3 1/2 hours. Add the beans and cook until tender, 15 minutes. Serve with assorted toppings and chips.
Keep the seeds in the chile peppers for this recipe-they add a nice amount of heat.