Preheat the broiler. In a large, heavy skillet, heat 1 1/2 tablespoons olive oil over medium heat. Add the scallions, carrot and half of the garlic and cook, stirring, until slightly softened, about 2 minutes. Move the veggies to the perimeter of the pan, add the pork to the center and cook over high heat, breaking the meat into clumps and turning occasionally until it begins to brown, about 5 minutes.
In a cup, combine 1/2 cup water, 3 tablespoons teriyaki sauce, the oyster sauce and cornstarch; pour over the pork and cook, stirring, until thickened, 1 to 2 minutes. Transfer the pork mixture to a bowl and keep warm.
In the same skillet, add the remaining garlic and 1 1/2 teaspoons olive oil and cook over medium heat for 1 minute. Add the swiss chard and remaining 1 tablespoon teriyaki sauce and stir-fry until wilted, about 3 minutes. Divide the chard among the bun bottoms. Spoon the pork mixture on top and cover with the bun tops. Serve with knives and forks.