In a large stockpot, over medium to high heat, add water, chicken, 2 teaspoons salt, 1 clove garlic, and quartered onion. Cover and simmer for about 30 minutes. Reserve.
Remove the chicken and allow it to cool. After the chicken cools off shred it. Reserve.
In a blender add the boiled onion and garlic clove, quartered tomato, chipotle peppers including adobo sauce, 2 teaspoons salt, and enough chicken broth to fill the blender half way. Puree 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, about 2 minutes.
Add chopped tomatoes and chopped garlic and cook for an additional 2 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 for 10 minutes.
Add salt to taste.
In a heavy skillet heat one-quarter inch of oil. Drop tortillas carefully into hot oil, one at a time, for 20 to 40 seconds on each side or until crisp and golden. Drain on paper towels. Store bought tostadas can also be used.
To assemble, place a tostada (fried tortilla) on a serving plate; spoon on Chicken Tinga, lettuce (optional), 1 or 2 slices of ripe avocado, crumbled queso fresco, and top with crema Mexicana or sour cream.
Garnish tostada with toppings of your choice.
Tinga is a tasty party dish that can be made a day ahead. It stores well in the refrigerator and tastes better the next day after the ingredients have marinated for a few hours.