Break and crack the bones of the carcasses.
Heat the vegetable oil in a 6-quart stockpot over medium-high heat. Season the bones with 1 teaspoon of the salt and the pepper. Add the bones to the pot and brown for about 10 minutes, stirring often.
Add the carrots, celery, onions, garlic, and the remaining teaspoon salt. Cook, stirring often, until the vegetables are soft, about 5 minutes.
Add the wine and tomato paste and stir to mix. Cook for 5 minutes, stirring occasionally. Add the water and the bouquet garni, and bring the mixture to a boil. Skim off any cloudy scum that rises to the surface, then reduce the heat to medium and simmer, uncovered, for 3 hours.
Strain the stock through a fine-mesh strainer and let cool. Refrigerate for 8 hours or overnight, then remove any congealed fat from the surface. The stock will keep in the refrigerator for 3 days or in 1- to 2-cup containers in the freezer for up to 1 month.
Yield: 4 cups