Place pork shoulder in a slow cooker along with 4 tablespoons soy sauce. Add cold water to cover (about 6 cups) and set on high heat. Cover and cook 4 hours or until tender.

Peel and julienne carrots. Submerge in 6 tablespoons water, cider vinegar, olive oil, and remaining 1 teaspoon soy sauce. Marinate at least 1 hour and up to 1 week.

Once tender, remove pork shoulder from cooking liquid; cool. Ladle cooking liquid into a separate container and set aside. When pork is cool enough to handle, shred meat from bone using a fork. Divide shredded pork into two equal portions, reserving one for future use.

Mix Sriracha with one portion of the pork to taste. Top four of the bread slices with pork; drizzle with about 1 tablespoon cooking liquid (reserve remaining liquid for another use; such as soup stock). Top with pickled carrots and remaining bread slices.