Place 3 tablespoons of butter in a medium saucepan and melt over medium heat.
Add the flour to the butter and stir until a thick paste forms and it begins to pull away from the sides of the pan.
Gradually pour in the milk, a little at a time, while stirring constantly to avoid lumps.
Add the salt and continue stirring until the mixture thickens to a pudding-like consistency.
Remove from heat and set aside for the soup.
For the Soup:
In a large saucepan, melt 2 tablespoons of butter over medium heat.
Add the sliced onions and cook, stirring frequently, until they are soft and translucent but not browned.
Pour in the chicken broth and add the chicken bouillon cubes, salt, and pepper. Stir until the mixture is heated through.
Add the prepared white sauce and Velveeta cheese to the soup. Stir constantly over medium-low heat until the cheese is fully melted and the ingredients are well combined.
Reduce the heat to warm and let the soup cook for 30–45 minutes, stirring occasionally.
Serve hot, garnished with shredded Cheddar cheese.
Notes
Tips and Tricks
Cooking the Onions
Cook the onions slowly over low heat to achieve a soft texture without browning them. Stir often to prevent burning.
Preventing Lumps in White Sauce
Add the milk gradually while stirring constantly to ensure a smooth, thick sauce.
Cheese Garnish
Shred the Cheddar cheese finely for easy melting on top of the hot soup.
How to Store and Reheat
Let the soup cool completely before transferring it to an airtight container. Store in the refrigerator for up to 3 days.Warm the soup on the stove over low heat, stirring occasionally, until heated through. Avoid high heat to prevent curdling.Freeze in a freezer-safe container for up to 2 months. Thaw overnight in the refrigerator before reheating.