In a large pot, melt the butter over medium heat. Add the chopped onion and minced garlic, sautéing until they become translucent and fragrant, about 3-4 minutes.

Stir in the flour and cook for 1-2 minutes, stirring constantly to form a roux.

Gradually pour in the chicken broth, stirring until the mixture is smooth and begins to thicken.

Add the broccoli florets and cook for about 5-7 minutes until they are tender.

Reduce the heat to low, stir in the milk, and allow it to warm through.

Add the cheddar cheese and cream cheese, stirring until melted and creamy.

Season with paprika, ground mustard, cumin, salt, and pepper to taste.

For a smoother texture, use an immersion blender to blend to your desired consistency or leave it chunky for added texture.