Influenced by his Turkish-American wife, Meltem, Scott Conant spices up his silky potato soup with Turkish red-pepper paste (biber salcasi), made from sweet and hot peppers. Look for the paste at Middle Eastern groceries, or use harissa instead.
In a large pot, heat 2 tablespoons of the olive oil. Add the shallots and a pinch of salt and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the potatoes and cook, stirring, until barely softened, about 5 minutes. Add the chicken stock and simmer over moderate heat until the potatoes are tender, about 20 minutes. Strain the broth into a heatproof bowl and transfer the shallots and potatoes to a blender. Add 1/4 cup of the olive oil and 1 cup of the broth and puree until smooth. Return the puree to the pot. Stir in the remaining broth and season with salt. Bring the soup back to a simmer over moderate heat.
In a medium bowl, toss the shrimp with the pepper paste and the remaining 2 tablespoons of olive oil. Season with salt. Add the shrimp to the soup and cook just until they are pink and curled, about 1 minute. Ladle the soup into bowls, garnish with the scallions and serve.