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Place the chopped broccoli, diced onion, minced garlic, broth, thyme, and nutmeg into the slow cooker. Season with a pinch of salt and pepper.
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Cover and cook on low for 4 to 6 hours or on high for 2 to 3 hours, until the broccoli is very tender.
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Once the broccoli is soft, use an immersion blender to blend the soup directly in the slow cooker until it reaches your desired consistency.
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You can blend it until completely smooth or leave a few small chunks of broccoli for texture.
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If you do not have an immersion blender, carefully transfer the soup in batches to a standard blender and return it to the slow cooker.
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Stir in the cornstarch slurry, heavy cream, and shredded cheddar cheese.
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Cover the slow cooker and cook on high for an additional 20 to 30 minutes. This allows the soup to thicken and the cheese to melt completely into the base.
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Give the soup a final stir, taste for seasoning, and add more salt or pepper if needed. Serve warm with crusty bread or crackers.
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Add crunch and color to each bowl with simple toppings. Try toasted pumpkin seeds or chopped walnuts for texture; sprinkle them just before serving so they stay crisp.
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For extra flavor, grate sharp cheddar or crumble feta over the hot soup. The cheese will melt slightly and add savory depth.
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Fresh herbs lift the dish: chop parsley, chives, or dill and scatter a teaspoon or two per bowl. A small drizzle of olive oil or a light swirl of crème fraîche will add silkiness.
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If you want heat, add a few red pepper flakes or a dash of hot sauce. For a low-calorie option, lemon zest and cracked black pepper brighten the soup without extra fat.