In a large pot, melt the butter over medium heat. Once it’s melted and sizzling a little, toss in the minced garlic. Let it sauté for about 1-2 minutes just enough to smell amazing. Don’t let it burn! Burnt garlic = sad soup.
Pour in your heavy cream and bring it to a gentle simmer. Then, add your vegetable or chicken broth. This combo is where all that creamy richness starts to build. Let it come back up to a simmer nothing too aggressive.
Add your chopped broccoli, grated carrot, and diced potato to the pot. (Tip: cut everything fairly small so it cooks quickly and evenly.) Let everything simmer together for 25–30 minutes, until the broccoli is tender and the potatoes are soft. This is a great time to check in on homework, load a dishwasher, or sip some tea and pretend you’re relaxing.
Once everything’s cooked, stir in the shredded cheddar cheese. Give it a moment to melt into that creamy base this is where the magic happens. Stir gently and patiently. You’ll see the soup thicken and transform into something that feels like a warm blanket.
Add salt and pepper to your liking. Taste as you go sometimes the cheese adds enough salt, sometimes it needs a little more love. You’re the boss of your soup.
Ladle that beautiful soup into bowls and, if you’re feeling fancy, top it with a little extra cheese or even a few croutons. Serve it with crusty bread, or keep it simple with crackers. Either way, it’s going to be a hit.