Korean Braised Beef Sandwich

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4 pounds beef chuck, cut into palm-sized pieces

3 tablespoons kosher salt

1 tablespoon ground black pepper

3 tablespoons canola oil

2 medium onions, chopped

2 carrots, chopped

6 cloves garlic

One 2-inch piece ginger, peeled and sliced diagonally

1 cup low-sodium beef broth

1 cup low-sodium soy sauce

1/2 cup light brown sugar

1/4 cup dried shiitake mushrooms, optional