Remove the meat from the rabbits, tear or cut into small pieces, and set aside. Discard the bones or reserve for another use.
In a large sauté pan, melt the butter over medium-high heat. Add the onions, celery and bell peppers, and cook until soft, 4 to 5 minutes. Add the mushrooms, salt and 1 teaspoon of the pepper, and cook, stirring, until soft and they have given up their liquid, about 6 minutes. Add the brandy and stir to deglaze the pan. Add the veal stock and cook until thickened, about 2 minutes. Remove from the heat and let cool completely.
In a large bowl, combine the rabbit meat, cooled onion mixture, the bacon, fat back, garlic, coriander, chili powder, kosher salt, remaining teaspoon of pepper, basil, oregano and thyme. Stir well to mix. Tightly cover with plastic wrap and refrigerate at least 6 hours, or overnight.
Preheat the oven to 325° F. Line a 12- x 3- x 4-inch terrine with plastic wrap. Bring a kettle of water to the boil.
In a small bowl, beat the egg with the heavy cream. Add the bread and soak until dissolved. Combine with the rabbit mixture.
In 2 batches in a food processor (or with a meat grinder, or the grinder attachment on a mixer), pulse to grind the rabbit mixture to a coarse texture. Pour into the prepared terrine and cover with the plastic wrap.
Wrap the terrine with a 2nd sheet of plastic, and then tightly in a heavy aluminum foil to make airtight.
Place the terrine in a medium roasting pan and transfer to the middle rack of the oven. Pour the hot water into the pan, reaching halfway up the sides of the terrine.
Bake until the terrine is cooked through, 1 hour and 45 minutes to 2 hours.
Carefully remove the pan from the oven and remove the terrine from the pan. Unwrap the foil to allow the terrine to cool to room temperature, or refrigerate before slicing.
Yield: 1 terrine, 8 to 10 servings
In a large, regular surface (not non-stick) sauté pan, heat the oil over high heat. Add the onions, sugar, thyme, salt and pepper, and sauté until starting to caramelize, about 10 minutes. As the onions caramelize, add the vinegar and water in stages, stirring and scraping the edges of the pan, until the onions are very soft and completely caramelized, about 30 minutes.
Remove from the heat and cool at least 15 minutes before serving with the terrine.
Yield: about 3 cups