Step 1

Heat the olive oil in a large stockpot over medium-high heat. When the oil is hot, add the chopped vegetables and cook, stirring often, until they are all soft, but not browned. This should take about 10 minutes or so.

Step 2

Add the white wine and all the remaining ingredients, plus enough water to cover everything by about an inch or two. Bring to a simmer, then drop the heat to a bare shimmy, about 175°F if you want to be precise. It should not boil under any circumstances, and keep an eye on things to ensure that it doesn't. Simmer like this for 45 minutes to 1 hour, no more.

Step 3

Turn the heat as low as it will go. Set a fine mesh strainer over a big bowl, then put a piece of paper towel or cheesecloth in the strainer. Ladle the stock through this set-up into the bowl. When you get to the bottom, skip the dregs down there, as they will be filled with sediment. The stock will never be as good as it is right now, but it can be refrigerated for up to a week and frozen for up to 6 months.