Preheat oven to 350°F (175°C) and grease a 9x13-inch baking dish.
Cook the lima beans according to package directions, but reduce the cooking time by 2-3 minutes. Drain thoroughly and set aside.
In a large saucepan, melt 4 tablespoons of butter over medium heat. Add the diced onion and cook until translucent, about 4-5 minutes. Add the minced garlic and cook for another 30 seconds until fragrant.
Sprinkle the flour over the butter and onion mixture, stirring constantly for 1-2 minutes to cook out the raw flour taste.
Gradually whisk in the milk and broth, ensuring no lumps form. Continue cooking and stirring until the mixture thickens enough to coat the back of a spoon, approximately 5-7 minutes.
Remove the pan from heat and stir in 3/4 cup of cheddar cheese, 1/4 cup of Parmesan, sour cream, dried thyme, and smoked paprika until smooth. Season with salt and pepper to taste.
Gently fold the cooked lima beans into the cheese sauce, ensuring they're evenly coated. Transfer this mixture to the prepared baking dish, spreading it into an even layer.
Melt the remaining 4 tablespoons of butter and mix with the cracker crumbs, remaining cheese, and 1 tablespoon of parsley. Sprinkle this mixture evenly over the bean mixture.
Bake uncovered for 25-30 minutes until bubbly around the edges and golden brown on top.
Allow the casserole to rest for 5-10 minutes before serving. Garnish with remaining fresh parsley.