Put the ground beef or any meat equivalent you want (either ground turkey, chicken, or bacon) in a medium pot.
Cook over medium heat until it turns slightly brown. Then, drain to remove any liquid present. Keep it aside.
Put a quarter quantity of butter in a large pot over medium heat and let it melt.
Add the onions, carrot, celery, basil, and garlic salt. Stir and let it heat until tender, which should take about 10 minutes.
Add the cooked ground beef to the veggies and stir evenly using a spatula.
Add the potatoes, chicken broth or chicken base to the large pot containing the beef and veggies. When using the chicken base, stir properly, add the ¼ pound of water, and stir.
Reduce to low heat and allow it to simmer with the pot covered until the potatoes are tender, which will take about 10-12 minutes.
Add the rest of the butter to a skillet, let it melt, and add the flour. Whisk thoroughly until it’s evenly mixed.
Cook and stir until it bubbles, which should take about 3-5 minutes.
Add the milk in small quantities and stir.
Keep stirring and adding the milk until the mixture is finely thinned out, ensuring no lumps are present.
Add the cheese to the bechamel sauce and stir until it melts.
Add the dry mustard and stir. This mixture can also be referred to as cheese sauce.
Add the cheese sauce to the rest of the soup and allow it to boil.
Cook and stir for about 2 minutes.
Reduce the heat, put in salt and pepper to taste, and stir.