Cut cauliflower into florets (about 3 cups). Cook in boiling salted water to cover 10 to 12 minutes or until tender; drain and set aside.
Melt 4 tablespoons butter in a medium saucepan over medium-high heat. Whisk in flour until smooth. Gradually add milk, whisking constantly, until mixture begins to thicken. Add cheese and sour cream, stirring until cheese melts. (Do not boil.)
Stir cauliflower, ham, and mushrooms into cheese sauce; pour into a 2-quart baking dish. Sprinkle breadcrumbs evenly over casserole. Cut 1 tablespoon butter into pieces, and sprinkle evenly over breadcrumbs.
Bake casserole, uncovered, at 350° for 45 minutes.