Don't bother peeling the onions, their skins add a nice, rich brown color to this vegetable stock. IF you'd like, remove the skins for use in dishes when a lighter color is preferred, such as in risotto or cream sauces.
1. Heat oil in a large stockpot over medium-high heat. Add remaining ingredients and cook, stirring occasionally, until vegetables begin to soften, 5-7 minutes. Add 4 quarts cold water. Bring to a boil; reduce heat and simmer until stock is reduced by half, 1 to 1.5 hours.
2. Strain stock through a fine-mesh sieve into a large bowl; discard solids. DO AHEAD: Stock can be made 3 days ahead. Let cool completely, then cover and chill, or freeze for up to 3 months.