Heat the olive oil in a large stockpot over medium heat. Once the oil is hot, add the onions, celery, and garlic. Stir them often and cook for about 5 minutes, just until the vegetables start to soften and become fragrant.
Add the leeks and carrots to the pot. Continue cooking for another 5 minutes, stirring regularly so the vegetables soften evenly without browning too much. This step helps build a deeper flavor before the liquid goes in.
Pour in the water and add the mushrooms, parsley, thyme, salt, peppercorns, and bay leaf. Stir everything together and raise the heat until the broth comes to a boil.
As soon as it boils, reduce the heat to low and let it simmer uncovered for 1 hour. Keep the broth at a gentle simmer so the vegetables release flavor slowly without turning bitter.
Once the broth has finished simmering, remove the pot from the heat. Set a colander over a large bowl or pot and line it with cheesecloth, then carefully strain the broth through it.
Discard the cooked vegetables and herbs after straining. If using the broth right away, skim off any fat from the surface. For a cleaner finish, refrigerate the broth for several hours or overnight so the fat rises and can be removed easily.
Use the broth immediately in your favorite recipes, or let it cool completely before storing. Keep it in the refrigerator for up to 3 days or freeze it in smaller containers for longer storage.