In a skillet, heat the oil. Add the onion and a pinch of salt and cook over moderately low heat, stirring, until softened, about 10 minutes. Add the red wine, vinegar, honey and thyme and simmer, stirring, until the liquid has evaporated, 15 minutes. Season the onion jam with salt and pepper; discard the thyme.
Light a grill. Generously season the sirloin with salt and pepper. Mix gently, then shape into eight 1-inch-thick patties; season again with salt and pepper. Grill the burgers, turning once, until charred on the outside and pink within, about 3 minutes per side. Just before the burgers are done, top them with the Stilton. Transfer to a platter. Lightly grill the buns. Set the burgers on the buns. Top with the onion jam and lettuce and serve.