For the sauce: In a bowl, whisk together the tomato sauce, soy sauce, brown sugar, tomato paste, vinegar, garlic, ginger and hot sauce until blended. Reserve 1/2 cup for the Round 2 Recipe Stuffed Cabbage Rolls, or another use. Set the rest of the sauce aside.
For the sloppy joes: In a large skillet over medium heat, add the oil. When it is hot, add the onions and peppers and cook until they are soft, about 5 minutes. Push the vegetables to one side of the pan and add the ground pork. Break up any lumps and sprinkle with salt and pepper. Cook until the pork is lightly browned, about 5 minutes. If there is a lot of fat in the pan, spoon some of it out and discard.
Add the sauce to the pan, bring to a simmer and cook until the pork mixture has thickened but is still a bit loose, about 15 minutes. Reserve 1 cup of the mixture for the Round 2 Recipe Stuffed Cabbage Rolls, or another use.
To serve, remove 2 leaves from the cabbage, roll them up like a cigar and slice into very thin strips. Reserve the remaining cabbage for the Round 2 Recipe Stuffed Cabbage Rolls, or another use. Divide the sloppy joe mixture onto the hamburger buns. Garnish with the sliced cabbage. Top with the bun tops and serve immediately.