Add jalapeno, onion, garlic, chili powder, cumin, oregano, salt, vinegar, and lime juice to a blender and puree until smooth. Transfer to a small saucepan, and simmer on low until the mixture is slightly thickened, about 10 minutes. Let the paste cool. Place the pork shoulder in a large bowl or in a ziploc bag, coat the meat with the paste, and let it marinate in the refrigerator for at least 8 hours or overnight.
Place pork (with the marinade) in a slow cooker. Add beef broth, white vinegar, cinnamon stick, and bay leaves to the pot. Cover and cook on high until the meat is tender, about 7 hours. Discard the bay leaves and cinnamon stick. Remove pork and shred the meat with forks. Season with salt and pepper to taste.
To make the pico de gallo, combine tomatoes, onions, jalapenos, cilantro, garlic, and lime juice in a mixing bowl. Season with salt and pepper to taste.
Serve the shredded pork in tortillas, along with toppings like avocado slices, radish slices, and cheese.