Cut the sweet potatoes into 1-inch chunks. The exact size doesn't matter as long as the chunks are close to equal in size.

In a large pot, add the potatoes. Add enough water to cover the potatoes. Cook for about 20 minutes or until done. They are done if a paring knife easily pierces the potatoes.

Drain and add back into the pot. Add the chicken broth, milk, and the butter. Mash with a masher until smooth. You can also run an immersion blender through the mixture to make it extra smooth.

Preheat the oven to 400 degrees. In a large skillet, heat about 1 tablespoon of cooking oil over medium-high heat. Add the onions, peppers, and mushrooms. Cook, stirring often until the onions are softened, about 5 minutes.

Season with salt and pepper and stir in the gochuhang and ketchup. Stir until the vegetables are coated. Add the ground beef, breaking it up with a wooden spoon, until cooked through.

Add 1 cup chicken broth and bring to a high simmer. Stir often and cook until the liquid is slightly reduced. Sprinkle the flour over the mixture and stir to combine and let the mixture thicken a bit.

Stir in the green onions. Season with salt and pepper if needed.

Transfer the beef mixture to a 2-quart baking dish. Spoon and top with the mashed sweet potatoes. Carefully spread the potatoes to cover the meat mixture.

Bake until the potatoes are browned and the meat mixture starts bubbling, about 25-30 minutes.