Sauté the Vegetables: In a large skillet, melt 2 tablespoons of butter over medium heat. Add the diced onions, sliced bell peppers, and minced garlic. Cook for 5–7 minutes, stirring occasionally, until the vegetables are soft and fragrant.

Brown the Beef: In a separate pan, quickly sear the thinly sliced beef over medium-high heat until lightly browned but still tender, about 2–3 minutes. Remove from heat and set aside.

Make the Creamy Base: Sprinkle 3 tablespoons of all-purpose flour over the sautéed vegetables. Stir for 1 minute to cook out the raw flour taste. Gradually pour in 4 cups of beef broth, whisking constantly to prevent lumps. Bring to a gentle simmer until slightly thickened.

Add Half-and-Half: Pour in 1 ½ cups of half-and-half, stirring to combine. Simmer for 2–3 minutes, allowing the soup to become creamy and smooth.

Combine Beef and Cheese: Return the browned beef to the pot. Add 1 ½ cups shredded cheddar cheese gradually, stirring until fully melted.

Season to Taste: Add salt, pepper, and 1 tablespoon of Worcestershire sauce (optional). Taste and adjust seasoning as needed.

Serve Hot: Ladle the soup into bowls. Garnish with extra shredded cheddar, chopped parsley, or green onions if desired. Serve immediately with toasted bread, rolls, or a side salad for a comforting meal.