Assist with whisking in the milk gradually. In about 5 minutes, or when the sauce begins to thicken, increase the heat to medium and whisk constantly.
Melt the shredded cheddar cheese by adding it to the sauce and tossing it in. Garlic pepper and salt should be added now.
After the vegetables have simmered, stir in the cheese sauce until well combined.
Add more milk to make the soup the consistency you want if you want it thinner. It may be necessary to add more salt and garlic pepper based on your taste evaluation.
Chopped bacon and more cheese, if you so wish, may be added as a final touch.