Roasting the vegetables yields rich and flavorful results.
Preheat oven to 425 degrees F.
Combine carrots, onions and fennel in a large roasting pan. Toss with oil. Transfer half the vegetables to a second roasting pan. Roast the vegetables for 45 minutes, stirring every 15 minutes and switching the position of the pans each time you stir.
In one pan, push the vegetables to one side and spread tomato paste in the other side. Continue roasting (both pans) until the tomato paste begins to blacken, 15 minutes more.
Transfer the roasted vegetables to a large stockpot. Pour 1/2 cup wine into each roasting pan and bring to a boil over medium-high heat. Cook, scraping up any browned bits, for 1 to 2 minutes. Add the contents of the roasting pans to the stockpot, along with water, celery, parsley, thyme, peppercorns, garlic and bay leaves. Cover and bring to a simmer. Uncover and simmer for 1 hour without stirring, adjusting heat as necessary to maintain the simmer (if the stock boils it will become cloudy).
Strain the stock through a colander, pressing on the solids to remove all liquid. Discard solids. Let the stock cool before storing.
To make ahead: Cover and refrigerate for up to 1 week or freeze for up to 3 months.
Equipment: 2 roasting pans
Nutrition Note: After straining and skimming, stock has negligible calories and nutrients.