In a large bowl, combine chiles and hot water; let stand 30 minutes. In a blender, puree 1 onion half, the tomato, garlic, bouillon, peppercorns, thyme, oregano, cumin and soaked chiles with soaking liquid until smooth. Strain through a fine sieve.
Place chicken in a Dutch oven; sprinkle with salt and pepper. Add bay leaves and remaining onion half. Add strained sauce and 2 cups cold water; stir to combine. Refrigerate, covered, 2 hours or up to 24 hours.
Place Dutch oven over medium heat. Bring mixture to a boil; reduce heat and simmer, covered, until chicken is tender and starting to fall apart, 1-1/2 to 2 hours. Remove meat and set aside; remove onion pieces and bay leaves and discard. Continue to simmer liquid, uncovered, until reduced by half, about 30 minutes. Shred meat with 2 forks; return to pan.
To serve, dip a tortilla into the meat mixture, thoroughly coating with sauce. Place the tortilla onto a griddle, comal or cast-iron skillet over medium heat. Sprinkle with cheese if desired; cook until cheese melts. Top with chicken; fold tortilla over to form a taco. Serve with toppings as desired.