In a medium sized pot: place chicken, 6 cups of water, 2 teaspoons of salt, 1 garlic clove, and 2 quarters of an onion. Cover and simmer for about 30 minutes on medium to high heat. Reserve the stock. Allow the chicken to cool and then shred it.
In a blender add the remainder of the quartered onion and 1 tomato, a can of chipotle peppers in adobo sauce, 2 teaspoons of salt and 1 chopped garlic clove, and enough chicken broth to fill the blender half way and blend until smooth.
Heat the oil in a large and deep pan over medium heat. Once it is hot but not smoking, stir in the chopped onion and cook until soft and translucent, for about 5 to 6 minutes. Then add chopped tomato and cook for an additional 10 minutes. Add the cooked shredded chicken, the chipotle sauce from the blender and more chicken broth if it is too dry. Bring to a boil, reduce heat and simmer covered for 10 minutes. Add salt to taste.
In heavy skillet heat one-quarter inch oil. Fry tortillas, one at a time, in hot oil for 20 to 40 seconds on each side or till crisp and golden. Drain on paper towels. Keep warm in foil in 250 degrees oven. Store bought tostadas can also be used.
To assemble each tostada, place a warm tortilla on serving plate; spoon on Chicken Tinga, then lettuce (optional), 1 or 2 slices of ripe avocado and crumbed queso fresco and Mexican Cream or sour cream. Drizzle with your favorite homemade salsa to taste.