Add the broccoli stem slices and saute until softened.
In the meantime, blanch the broccoli tips in a pot of boiling water over medium heat until bright green. Remove the tips from the water and "shock" in a bowl of iced water.
Drain the green tips and puree in a blender. Set aside.
Puree the soup in a blender and strain through a fine chinoise into a large serving bowl.
Add the green tip puree and season with salt and pepper, to taste.
Serve piping hot.
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