In a large pot, melt butter over medium-high heat. Add diced celery and onion, cooking until softened, about 5 minutes.

Sprinkle in the flour, stirring until the vegetables are coated and the flour is no longer visible, roughly 2 minutes.

Gradually pour in the half-and-half, followed by the chicken broth, stirring constantly to combine and prevent lumps.

Bring the mixture to a simmer, then add the shredded chicken, cheddar cheese, and hot sauce. Season with salt and pepper to your liking.

Reduce heat to medium-low and continue to simmer, stirring occasionally, until the cheese is fully melted and the soup is heated through, about 10 minutes.