PUT the broccoli in your food processor and process it until it’s very well chopped but there are still a few bigger pieces for texture. Transfer it to a Dutch oven or soup pot.
ADD your carrots and a little broth to the pot and set it over medium-high heat.
ADD your chopped onion and some butter (to add flavor and a smooth texture) and enough broth that the liquid comes up to the level of the vegetables but doesn’t cover them. Save a little broth for the end, in case your soup is too thick.
ADD as much garlic powder as you want, a couple pinches of smoked paprika, and a pinch of salt. Go ahead and stir it all together while bringing it to a gentle boil.
REDUCE the heat and boil gently for about 10 minutes, until the vegetables become nice and tender. Can y’all smell that? Oh yes, God have mercy!
ADD the cheddar. Use a lot here, honey. Go on ahead and add the whole bag if your spirit tells you to. Add the yogurt, plus a little more paprika and garlic powder if you want to, because that’s your business.
STIR until the cheddar has melted and the yogurt is well blended. If the soup is too thick, add a little of that broth you held back.
REDUCE the heat to medium and simmer for 5 to 7 minutes to let all those flavors dance together. Season to taste.
LADLE it into a bowl, top with some croutons and cilantro or parsley, if you want to, and enjoy!