Melt butter in a large pot over medium heat. Add onion; cook until softened, 3 to 5 minutes. Add chicken broth and cauliflower; bring to a boil.

Reduce heat slightly; simmer until cauliflower is tender, 20 to 30 minutes.

Meanwhile, grate Cheddar cheese. Whisk milk and flour together in a bowl.

When cauliflower is tender, slowly add milk-flour mixture, stirring until combined. Simmer until soup thickened, about 5 minutes.

Off heat, stir in Cheddar until melted and combined; season with salt and black pepper.