Poach the chicken: Place chicken in a pot with broth, bay leaf, and 1 tsp salt. Add water to cover. Bring to a gentle simmer (not a boil) and cook 15-20 minutes until 165°F. Remove chicken, reserve 1 cup poaching liquid, discard bay leaf.
Shred: When cool enough to handle, shred chicken with two forks into bite-sized strands.
Caramelize onions: In a large skillet over medium heat, warm olive oil. Add sliced onions and cook 8-10 minutes, stirring occasionally, until soft and golden at edges. Add garlic, cook 1 minute more.
Build sauce: Add chipotles, adobo sauce, crushed tomatoes, oregano, and 1 cup reserved poaching liquid. Simmer 10 minutes, stirring occasionally, until slightly thickened.
Combine: Add shredded chicken to sauce, toss to coat. Simmer 5 minutes. Season with remaining 1/2 tsp salt. Serve on tostadas with toppings.