This recipe makes more than you'll need for many recipes, but the stock can be frozen for up to four months. The gelatin from the rabbit bones is released during the long cooking time yielding a rich, flavorful stock.
Preheat oven to 450 degrees. Place rabbit bones on a rimmed baking sheet and roast until browned, about 1 hour.
Heat oil in a large stockpot over medium-high heat. Add onions, carrots, and celery. Cook until softened and beginning to brown, about 10 minutes. Stir in tomato puree, and cook, stirring constantly, until beginning to brown. Add wine and cook until completely evaporated. Add peppercorns, bay leaves, browned bones, and water. Bring to a boil, add thyme sprigs, and simmer until reduced and thick enough to coat the back of a spoon, at least 6 hours and up to 8 hours. Strain through a fine sieve, and discard solids. Store in an airtight container in the refrigerator for up to 3 days or frozen for up to 3 months.