NOTE: White rice flour is my preferred way to thicken gluten-free sauces and soups. Gluten-free flour blends can be used too but, I have found that different gluten-free flours (even different brands of rice flour) will give varying thickening results. If the soup is not thick enough after stirring in the cheese in step 9 and you don't plan to puree it, here is how to thicken it more:Make a paste of equal parts of soft butter and flour, mixing them together until all of the flour is moistened. Use 1 Tbsp of each for a little extra thickening or 2 Tbsp each for a lot of thickening. Drop this paste into the warmed soup and stir over medium high heat until the liquid boils and thickens. If leaving the soup chunky, cut the broccoli into very small bite-sized pieces. If using frozen, let it thaw at room temp on an absorbent kitchen towel for 5-10 minutes. Then cut while partially thawed. If you plan to puree the soup, I recommend leaving some larger pieces of broccoli. This way you can easily pull them out before pureeing and chop up for a garnish. Mince the onion and celery.
Heat a 2 quart pot over a high flame for a minute or two. Add about 2 teaspoons of the butter and melt.
Turn the flame to medium and add the celery and broccoli. Cook for 2 minutes.
Add the onion and cook, stirring, for another 2-3 minutes or until the onions turn translucent, Do not brown, Turn the heat down if the onions start to brown.
Add the remaining butter and melt. Add the flour and stir with a wire whisk, The mixture will turn thick and pasty. Keep cooking and stirring until it loosens up a little, about 1-2 minutes.
Pour in 2 cups of the milk and all of the broth and turn the heat to high. Stir every 30 seconds or so until the liquid boils and thickens. Turn the heat to medium and cook, stirring constantly for another minute,
Remove from the heat and stir in the cheese and black pepper, if using. Stir until it is melted and the mixture is smooth.
If you want your soup less chunky or completely smooth, pull out the larger pieces of broccoli (if you want some for garnish) and blend with an immersion blender or in a high powered blender. **When using the blender, be sure to remove the center piece from the lid (or open the spout) to allow steam to escape. Because different cheeses and broths will add varying level of saltiness, I have not given an exact amount of salt. First take a taste of the soup. Is it a little blah? Are the flavors not POPPING? Start with 1/8 tsp salt. Stir it in and taste again. I usually use between 1/8 and 3/8 tsp salt.
If you are serving immediately and the soup is too thick, stir in the remaining 1/4 c milk.