Warm butter and oil over medium heat in a large (16 quart) stock pot. Once the butter starts foaming, add carrots, onion, celery, garlic and mushrooms, stirring to coat in fat.

Let the vegetables cook for a few minutes until they start to caramelize (no stirring!). Once you see the vegetables getting some color, stir. Repeat this process until a good portion of the vegetables are caramelized (10 to 15 minutes).

While the vegetables are cooking, bundle up thyme, parsley, basil and bay, securing with kitchen string.

Add white wine to the stock pot and scrape up any brown bits stuck to the bottom. Let simmer until most of the liquid cooks off.

Add herb bundle, toasted peppercorns, chicken carcasses and water. Increase heat to medium-high and cook until you start seeing bubbles rise to the surface (10 to 15 minutes). Do not boil! Drop heat to low and cook for 2 and 1/2 hours without stirring. Skim off any foam that may rise to the surface during the first 10 minutes of cooking.

Carefully strain the stock through a medium-mesh strainer to remove all of the big solids. Discard solids. Strain again through a fine-mesh strainer to remove all of the small particles.

Let mixture cool before transferring to the refrigerator. You can rapidly chill the stock by floating the bowl in a sink filled with ice and cold water. Stir the stock occasionally until chilled.

Refrigerate the stock for several hours (or overnight) then skim any fat that congeals on the surface. Store in the refrigerator for up to 5 days or the freezer for several months.