Pierce each sausage in two or three places to prevent bursting during cooking.

Parboil sausages in a covered frying pan with about 1 inch of water for 10 minutes to cook them through.

Drain the water from the pan.

Lightly brown the sausages over medium heat. Do not add oil; the sausage's fat will be sufficient.

Add the sliced onions, chopped tomatoes, sliced celery, sliced sweet peppers, sliced mushrooms, and finely diced garlic to the pan.

Sprinkle with chili powder, thyme, oregano, sugar, and vinegar.

Stir all ingredients well to combine.

Cover the frying pan and let the mixture simmer until the vegetables are tender, approximately 20 minutes.