1. In a large soup pot set over medium-high heat, add the oil, onions, carrots, celery and 1 teaspoon salt and cook, stirring often, until the vegetables become very soft and start to brown and stick to the bottom of the pan, about 20 minutes.

2. Stir in the parsley stems, garlic, 1 teaspoon salt and the pepper and cook until the garlic is fragrant, 2 to 3 minutes. Add the water and chicken carcass along with any skin, fat and leftover meat shards, increase the heat to high and bring the water to a boil. Reduce the heat to medium-low and simmer, partially covered, until the stock is full-flavored and rich, 1 hour to 1 hour and 15 minutes (or up to 3 hours for a super concentrated, rich stock). Turn off the heat and cool for 30 minutes before straining through a fine-mesh sieve into an airtight container. Cover and refrigerate for up to 5 days.