Prepare a grill for medium-high heat. Lay two 18-inch-long sheets of heavy duty aluminum foil on a flat surface.
Cut a long lengthwise slit in each sausage about two-thirds of the way through and flatten gently so it opens like a book. Divide the sausages between the 2 pieces of foil. Toss the peppers and onions with the oil, oregano, 1 teaspoon salt and 1/2 teaspoon pepper and divide evenly between the foil pieces.
Fold and seal the edges of each packet. Grill 17 to 20 minutes; the sausages will be charred with grill marks on the bottom and the vegetables will be tender. Carefully open the packets, watching for the escaping steam. If necessary, throw the packets back on the grill, unsealed, for a few more minutes. Garnish with the parsley.
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