How to Make It
Prepare the collard greens: Heat oil in a large Dutch oven over medium-high. Add onion, and cook, stirring often, until translucent, 5 to 6 minutes. Add collard greens, and cook, stirring often, until beginning to wilt, about 1 minute. Add broth, salt, sugar, and cayenne. Cover and bring to a boil. Reduce heat to medium-low, and simmer, stirring often, until tender but slightly toothy, 35 to 40 minutes. Stir in vinegar. Set aside.
Prepare the burgers: Place sausage in a food processor; pulse until finely chopped. Place sausage, beef, and salt in a bowl, and stir to combine. Form into 4 (½-inch-thick) patties.
Preheat grill to high (450°F to 500°F). Place burgers on oiled grates. Grill, uncovered, 6 minutes, turning once halfway through.
Prepare the fried oysters: Heat oil to 360°F in a heavy saucepan. Place buttermilk and oysters in a bowl. Combine all-purpose flour, corn flour, and cornmeal in another bowl. Using a slotted spoon, transfer oysters from buttermilk to flour mixture, letting excess buttermilk drip off before placing in flour mixture; toss to coat. Carefully place oysters in hot oil, and fry until crispy, 2 to 3 minutes. Drain on paper towels, and sprinkle with salt.
Place 1 burger on each of the 4 bottom buns. Top each with ¼ cup drained collard greens, 3 fried oysters, 2 tablespoons chow-chow, and top bun.