1) Over a medium grill take garlic and chiles on a bamboo skewer turn occasionally until blackened. Transfer garlic and chiles into a medium bowl, cover with plastic wrap and let cool. Peel, core and seed the chiles and cut into ¼ inch strips. Peel the garlic cloves.
2) Transfer the garlic and two-thirds chiles to a blender. Add the cilantro, lime juice, cumin, oregano and water and puree until smooth. Season the sauce with salt and pepper and transfer to a small saucepan. Simmer over moderate heat, stirring occasionally, until the sauce is slightly thickened, about five minutes. In a small bowl, combine the remaining roasted chiles with the cheese.
3) Shape Bison into patties ¾ inch thick and season generously with salt and pepper. Grill over medium heat 4 minutes each side. Brush buns with oil and toast over grill on cut sides of buns
4) Set the grilled burgers on the bottom halves of the buns. Top the burgers with the chile-cheese mixture and a generous spoonful of the salsa verde. Cover the green-chile burgers with the buns and serve right away, passing the remaining salsa verde on the side.