Begin by soaking the dry lima beans in cold water overnight. This process helps to soften the beans and reduce their cooking time.

The next day, drain and rinse the soaked lima beans. Then, transfer them to a pot and cover them with fresh water.

Bring the water to a boil, then reduce the heat to a simmer. Cook the beans until they are tender, which typically takes about 1 1/2 hours.

Once cooked, drain the beans and mash them using a fork or potato masher. Set aside.

In a saucepan, melt the butter over medium heat. Add the chopped onion to the melted butter and sauté for about 3 minutes until the onion becomes soft and translucent.

Then, add the thinly sliced celery to the saucepan. Cover and continue to cook until the celery is tender, stirring occasionally.

Once the vegetables are tender, stir in the flour and cook for an additional 2 minutes. This helps to create a roux, which will thicken the mixture.

Gradually pour in the skim milk while stirring continuously. Allow the mixture to simmer until it thickens to a sauce-like consistency. Remove the saucepan from the heat.

Add the beaten egg to the saucepan and mix well to incorporate it into the sauce. Then, fold in the mashed lima beans, soft whole wheat crumbs, chopped peanuts, chopped carrots, salt, and black pepper. Stir until all ingredients are evenly combined.

Preheat the oven to 375°F (190°C) and grease an 8 x 4 inch loaf pan. Spoon the lima bean mixture into the greased loaf pan, spreading it out evenly.

Place the loaf pan in the preheated oven and bake for 35 to 45 minutes, or until the top of the loaf is golden brown and set.

Once the loaf is baked, remove it from the oven and arrange slices of American cheese on top.

Return the loaf to the oven and bake for a few more minutes, until the cheese is melted and bubbly.

Remove the lima bean loaf from the oven and let it cool for a few minutes before slicing and serving. This flavorful and nutritious dish is ready to be enjoyed!