In a stockpot, heat the butter over medium heat for 1 to 2 minutes. Add the onion, celery, carrots, and garlic and sauté for 2 to 3 minutes, stirring frequently.
Pour in the water and stir. Add the parsley, thyme, bay leaves, and salt and stir once more. Bring to a boil, then reduce the heat to a simmer and continue to simmer for 30 to 35 minutes.
Line a colander with cheesecloth and set over a heatproof container. Pour the stock through the colander into the container; discard the vegetables.
Store the vegetable stock in an airtight container in the refrigerator for up to 1 week, freeze for up to 2 months.