Heat oil in a large saucepan over medium-high heat. Add and cook the onion, garlic, thyme, bay leaf, parsley, and peppercorns, stirring often, until garlic is deep brown, about 5 minutes.
Add in your leftover veggies (if using) and saute until brown.
Add the cup of wine, bring to a simmer, and cook, scraping up any brown bits, until liquid is reduced by half, about 4 minutes.
Add Parmesan rinds and 8 cups water and bring the stock to a boil. Reduce heat and simmer, occasionally stirring to prevent any rinds from sticking to the pot, until broth is flavorful and reduced by half, about 2 hours.
Strain through a fine-mesh sieve into a large bowl (or an airtight container if making ahead).
Let cool; cover and chill.