Top each toast slice with Cheddar cheese. Melt cheese with a kitchen torch until bubbling and golden, 30 seconds. (See footnote for broiler instructions.)
Melt butter in a pot over high heat. Cook and stir garlic in hot butter until fragrant and sizzling, about 15 seconds. Add stock to pot and bring to a boil. Stir broccoli into stock, pushing broccoli down into liquid; return to a boil and cook until broccoli is tender, 7 to 8 minutes.
Puree broccoli mixture using an immersion blender until soup is smooth.
Stir cream, cayenne pepper, and salt into soup; puree with immersion blender again until smooth, about 30 seconds. Ladle soup into bowls and top with cheese toast.
If you don’t have a kitchen torch you can melt the cheese onto the toast in your oven’s broiler.
If you don’t have an immersion blender you can puree the soup in batches in a food processor or blender.
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