In a medium-sized pot, melt a couple of tablespoons of butter over medium heat. Sauté the onions until softened, add the potatoes, and cook for another 10 minutes. Add the rest of the vegetables, and cook for 5 more minutes.
Add the broth, salt and pepper, and bring to a boil. Lower the heat, and add the halibut. Allow to simmer for about 5 minutes.
Add the milk slowly, stirring continuously. Then add the flour and the remainder of the butter, and stir until the mixture thickens. Cook for another 8 minutes.
Stir in the cheese until it melts. Serve immediately.