1. Cook the Vegetables:

1. Preheat your oven to 375°F (190°C).
2. Bring a large pot of salted water to a boil. Add the diced potatoes and cook for 8 minutes.
3. Add the green beans to the pot and cook for an additional 4-5 minutes until both vegetables are tender but not mushy. Drain and set aside.

2. Prepare the Sauce:

1. In a large skillet, melt the butter over medium heat. Add the diced onion and sauté until softened, about 3 minutes.
2. Stir in the garlic and cook for 1 minute until fragrant.
3. Pour in the heavy cream and bring it to a gentle simmer. Add the cheddar cheese, Parmesan cheese, smoked paprika (if using), and a pinch of salt and pepper. Stir until the cheese is melted and the sauce is smooth.

3. Assemble the Casserole:

1. In a greased 9×13-inch casserole dish, combine the cooked green beans and potatoes.
2. Pour the cheese sauce over the vegetables and gently mix to coat evenly.

4. Add the Topping (Optional):

1. Sprinkle breadcrumbs over the top for a crispy finish. You can also mix the breadcrumbs with a tablespoon of melted butter for extra richness.

5. Bake:

1. Place the casserole in the preheated oven and bake for 20-25 minutes, or until the top is golden and bubbly.

6. Serve:

1. Remove the casserole from the oven and let it cool slightly before serving. Enjoy as a side dish or a light main course.