Preheat oven to 375F. Place cod in a greased baking dish.
Make the white sauce in a heavy saucepan. Melt the butter over medium heat and stir in the flour until smooth. Remove from heat and slowly stir in half of the milk, then return to heat and beat until smooth and shiny.
Gradually add the remaining milk, followed by salt, pepper, and your vegetables. Cook until sauce is smooth & thickened.
Pour sauce over the fish, and sprinkle breadcrumbs and cheese over the top.
Bake, uncovered for 20-30 minutes until sauce bubbles and the cheese begins to brown. Let rest 10 minutes after cooking completes.