Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish and set aside.

Cook the Potatoes and Green Beans: Place the diced potatoes in a large pot of salted water. Bring to a boil and cook for about 8-10 minutes, until the potatoes are just fork-tender. Add the green beans to the pot during the last 2-3 minutes of cooking to soften them slightly. Drain and set aside.

Prepare the Bacon (Optional): If using bacon, cook the slices in a skillet over medium heat until crispy. Transfer to a paper towel-lined plate to cool, then crumble and set aside.

Make the Sauce: In a large saucepan, melt the butter over medium heat. Add the diced onion and cook for 3-4 minutes until softened and translucent. Add the minced garlic and cook for another minute until fragrant.

Create the Roux: Sprinkle the flour over the onion and garlic, stirring constantly for about 1-2 minutes to cook out the raw flour taste. Gradually whisk in the chicken or vegetable broth until smooth, followed by the heavy cream. Continue to stir and cook for about 3-4 minutes until the mixture thickens.

Add the Cheese: Remove the sauce from the heat and stir in the shredded cheddar cheese and grated Parmesan until melted and smooth. Season with salt and black pepper to taste.

Assemble the Casserole: In the prepared baking dish, combine the cooked potatoes, green beans, and crumbled bacon (if using). Pour the cheese sauce over the top, gently stirring to coat the vegetables evenly.

Bake the Casserole: Place the baking dish in the preheated oven and bake for 25-30 minutes, or until the casserole is bubbly and the top is golden.

Garnish and Serve: Remove from the oven and let cool slightly. Garnish with fresh chopped parsley and serve hot.