Step 1In a large saucepan, place the chicken breasts and add enough water to cover. Add the bay leaf, unpeeled garlic clove and small chunk of onion and bring to a boil. Cover and remove from heat. Set the pan aside until the chicken has cooked all the way through, about 20 minutes. Remove the chicken to a bowl, and set aside until cool enough to handle, then shred the meat with your fingers or a fork.
Step 2In a skillet heated over medium-high heat, add the oil. When the oil is hot, add the chopped onion and cook until translucent, stirring often, 3 to 5 minutes. Stir in the minced garlic and cook until aromatic, 15 to 30 seconds. Add the tomato, cooking until pieces break down and become a thick, chunky paste, about 5 minutes.
Step 3Stir in the shredded chicken, then add the chipotle, oregano and chicken broth, and season with three-fourths teaspoon salt, or to taste. Bring to a boil, then reduce the heat, cover and simmer about 10 minutes to thicken slightly and marry the flavors. Taste, and add more salt if desired. This makes about 2 cups of tinga de pollo.
Step 4To serve the tostadas, slather a thin layer of crema on each tortilla. (For more amped-up chipotle flavor, mix a little of the adobo sauce in the crema.) Add a few spoonfuls of tinga, the slices of white onion and two slivers of avocado. Top with crumbled cotija cheese.