In a large, heavy saucepan, over medium heat, cook the onion in the butter until softened, about 5 minutes.
Add the flour and stir until smooth. Whisk in the broth and milk, then add the sweet potato, bay leaf, thyme, ½ teaspoon salt, and ¼ teaspoon pepper.
Bring to a boil, reduce heat, and simmer, stirring occasionally, until the potatoes are just tender, about 8 minutes.
Add the salmon and broccoli and simmer until the salmon is cooked through and the broccoli is tender, about 5 minutes more.