In a large pot or Dutch oven, melt the butter over medium-high heat.
Once melted, add the diced onions and cook, stirring occasionally, until they become translucent.
Stir in the diced red bell peppers and chopped roast beef, cooking until the peppers soften.
Add the chopped garlic and cook for 2 minutes, stirring frequently.
Sprinkle in the flour and stir well, continuing to cook until the flour turns a light brown.
Pour in the beef broth, stirring thoroughly and scraping the bottom of the pot to loosen any browned bits. Continue cooking and stirring until the broth thickens slightly.
Add the half and half and stir to combine.
Mix in the Worcestershire sauce, salt, pepper, and paprika, stirring well.
Bring the soup to a boil, then immediately reduce the heat to medium-low. Let the soup simmer for 15 minutes, stirring occasionally.
While the soup simmers, combine the water and cornstarch in a small bowl, stirring until the cornstarch dissolves.
Pour the cornstarch mixture into the soup and stir well. Allow the soup to simmer for a few more minutes until it thickens.
Remove the pot from heat and stir in the shredded cheddar cheese until fully melted.
Serve hot and enjoy, optionally topped with extra shredded cheddar cheese, croutons, or French’s crispy fried onions.