Prepare the vegetables: Peel and quarter the yellow onions. Wash and roughly chop the carrots and celery stalks, including any leafy tops from the celery. Lightly smash the garlic cloves with the side of your knife. Gather the parsley stems and thyme sprigs.

Combine ingredients in a large stockpot: Add the prepared onions, carrots, celery, smashed garlic, parsley stems, thyme sprigs, and bay leaves to a large stockpot (at least 6-liter or 6-quart capacity).

Add water and peppercorns: Pour in the 3.75 liters (16 cups) of cold water, ensuring all the vegetables are submerged. Add the whole black peppercorns.

Bring to a boil and simmer: Place the stockpot over medium-high heat and bring the water to a rolling boil. Once boiling, immediately reduce the heat to low, cover the pot loosely, and let it simmer gently for at least 1 hour, or up to 2 hours for a more concentrated flavor.

Strain the broth: Carefully ladle the broth through a fine-mesh sieve set over a large heatproof bowl or another clean stockpot. Discard the solids. For an exceptionally clear broth, you can line the sieve with cheesecloth before straining.

Cool and store: Allow the strained vegetable broth to cool to room temperature before storing. Once cooled, transfer it to airtight containers. It can be refrigerated for up to 4 days or frozen for up to 3 months. You can also freeze it in ice cube trays for smaller portions.