Preheat oven to 350ºF. Lightly spray a 9x13-inch pan with cooking spray. Set aside.
In a large skillet, heat 1 Tbsp butter over medium-high heat. Add mushrooms and cook until tender. Remove from pan
In same pan, melt remaining 5 Tbsp butter over medium-high heat. Stir in flour until smooth. Slowly whisk in half-and-half. Bring to a boil, stirring constantly, cook until thickened, about 2 minutes. Reduce heat to low and stir in rosemary, salt and cheese. Stir until melted. Remove from heat.
Arrange potatoes in an even layer in bottom of prepared pan. Top with cooked mushrooms. Pour sauce over mushrooms and sprinkle with paprika.
Cover pan with aluminum foil and bake, covered, for 40 minutes. Remove foil from pan and continue baking for an additional 20 to 25 minutes.
Can assemble the casserole in advance and refrigerate overnight before baking.Can substitute Swiss cheese for Gruyere.I used a mixture of white mushrooms, shiitake, and baby portobello mushrooms in this casserole.