Heat 1 tablespoon (15 ml / 0.5 fl oz) of oil in a large pot or Dutch oven over medium-high heat.
Add the onion (or shallots/leek) and cook until soft, about 3 minutes.
Add the carrots and celery, season with salt and pepper, and cook, stirring frequently, until tender, about 10 more minutes.
Remove the vegetables with a slotted spoon and set aside.
Add the remaining 1 tablespoon (15 ml / 0.5 fl oz) of oil to the pot and increase the heat to high.
Add the chopped white mushrooms and cook, stirring, until they release their liquid and begin to brown deeply, about 10 minutes. This browning step is crucial for flavor.
Season the mushrooms with a pinch of salt, then return the cooked vegetables to the pot along with the dried mushrooms.
Stir to combine.
Pour in the water, and add the parsley stems and optional bay leaves. Scrape the bottom of the pot to release any browned bits.
Bring the mixture to a boil, then reduce the heat to maintain a strong, steady simmer.
Cook, partially covered, for about 30 minutes, allowing the flavors to meld and the stock to reduce slightly.
Carefully strain the stock through a fine-mesh sieve into a large bowl or container, pressing gently on the solids to extract all the liquid.
Discard the solids.
Use the stock immediately, or let it cool completely before storing in an airtight container in the refrigerator for up to 5 days or in the freezer for up to 3 months.
