Preheat the broiler. Broil the peppers, turning occasionally, until blistered and softened, about 8 minutes. Let cool slightly, then cut a long strip out of one side of each chile; chop up the trimmings. Gently seed the peppers to make charred pepper boats.
In a large skillet, heat the oil, one turn of the pan, over medium-high. Add the sausage and cook, breaking up with a spoon and stirring occasionally, until browned, about 5 minutes. Add the onion and chiles and cook, stirring occasionally, until softened, about 5 minutes. Add the garlic, cumin and chile trimmings. Cook, stirring often, until aromatic, about 1 minute. Add the tomato paste; stir until the color darkens, about 1 minute. Add the stock, reduce the heat to low and simmer until slightly thickened, 1 to 2 minutes. Stir in the parsley.
Divide the mixture among the chiles, top with the cheese and broil until golden, about 2 minutes.
