Heat the drippings or oil in a medium saucepan over medium heat. Add the scallion and cook, stirring, until tender, 3 to 5 minutes. Add the potato, cayenne, thyme, garlic, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring, until the potatoes are well coated, 2 to 3 minutes. Pour in the broth and bring to a simmer.
Add the broccoli and Poblano pepper and simmer until the potatoes and vegetables are tender, about 20 minutes, adjusting the heat as needed to maintain a simmer. Remove from the heat, discard the thyme stems and let cool at least 5 minutes. Carefully puree until smooth with a handheld immersion blender or in 2 to 3 batches in a blender (do not fill the blender more than halfway full).
Reheat the soup if necessary, and adjust the consistency with water and seasoning with salt and pepper as needed.
Serve hot with a dollop of sour cream, some cilantro and a sprinkle of cayenne pepper.
When blending hot liquid, first let it cool for 5 minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.
Copyright 2015 Television Food Network, G.P. All rights reserved.