Combine the garlic, oregano, salt, chili powder, cumin, and black pepper. Add olive oil and mix well. Use a mortar and pestle to make a paste consistency, or mash with a fork.
Wash chicken leg quarters and pat dry. Snip off any excess skin. Arrange the chicken pieces in a baking dish and pat the garlic mixture over each quarter. Pour 1/2 cup of chicken broth (part dry white wine, if desired) into the baking dish. Bake for 40 to 50 minutes, or until juices run clear.