Cook the Ground Beef:

1. Heat a large pot over medium-high heat and add the ground beef.
2. Add the diced onions to the pot and crumble the beef as it cooks. Cook until the beef is browned and fully cooked.

Make the Roux:

1. Once the beef is cooked, add the butter to the pot. Once the butter has melted, stir in the flour.
2. Cook the mixture for about 3 minutes, stirring constantly, to form a roux.

Add the Broth and Cream:

1. Gradually add the chicken broth to the pot, whisking constantly until a thick mixture forms.
2. Pour in the half and half cream, whisking until smooth.

Season the Soup:

1. Add the garlic powder, onion powder, salt, and pepper to the soup. Stir well to combine.

Add Potatoes and Simmer:

1. Stir in the frozen diced hash brown potatoes. Reduce the heat to medium and allow the soup to simmer, stirring frequently, for about 10 minutes until the potatoes are tender.

Finish with Green Onions and Cheese:

1. Add the chopped green onions and stir to combine.
2. Stir in the shredded cheddar cheese until fully melted and smooth.

Serve and Enjoy:

1. Serve the soup immediately, hot and cheesy!