In a medium saucepan, heat the 1 tablespoon of oil. Add the onion and ginger and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the garlic and cook for 1 minute, stirring. Add the tomato puree, ketchup, vinegar, Worcestershire sauce, mustard, honey, molasses, ancho chile powder, chipotle and water. Bring to a simmer and cook over low heat, stirring occasionally, until thickened, about 30 minutes. Transfer the sauce to a blender. Add the peanut butter and puree until smooth. Season the barbecue sauce with salt and pepper.
Light a grill or preheat a grill pan. Brush the cut sides of the buns with oil and grill until toasted, about 30 seconds. Spread some of the barbecue sauce on the buns.
Form the meat into four 1-inch-thick patties and brush with oil. Season with salt and pepper and grill over high heat, turning once, until nearly cooked through, about 5 minutes. Brush the burgers with some of the sauce and grill until lightly glazed, about 2 minutes. Top with the cheddar and scallion, close the grill and cook just until the cheese is completely melted, about 1 minute. Set the burgers on the buns, top with lettuce and tomato and serve right away.