Melt the butter in a large pot or Dutch oven over medium heat. Add the diced onion and cook for 4 to 5 minutes until softened and translucent. Add the garlic and cook for 30 seconds.
Sprinkle the gluten free flour blend over the onion and stir constantly for about 1 minute to form a roux.
Slowly pour in the chicken broth while whisking continuously, then add the milk and heavy cream. Stir until smooth and bring to a gentle simmer.
Add the chopped broccoli florets, onion powder, nutmeg, salt, and black pepper. Simmer for 12 to 15 minutes, stirring occasionally, until the broccoli is very tender.
Use an immersion blender to partially blend the soup, leaving some chunky broccoli pieces for texture. Alternatively, transfer about 2 cups of the soup to a blender, blend until smooth, and stir it back into the pot.
Remove the pot from the heat and stir in the shredded cheddar cheese a handful at a time, stirring after each addition until completely melted and smooth. Taste and adjust seasoning as needed. Serve hot.