Preheat the oven to 450°F (230°C). Toss the frozen corn with olive oil, salt, ground black pepper, and paprika. Arrange the corn in a single layer on a baking pan lined with parchment paper, smoothing it out evenly. Bake for 15 minutes until aromatic. Remove from the oven and set aside
Meanwhile, heat a heavy-bottomed pot (soup pot) over medium heat. Melt the butter in the pot, then add the onion and a pinch of salt. Sauté the onion for 3 to 5 minutes until aromatic and translucent.
Reserve one cup of roasted corn for serving. Add the remaining roasted corn and water to the pot. Gently stir and bring to a boil. Reduce the heat to medium-low, cover, and let it simmer for 15 minutes.
Puree the soup using a blender (or an immersion blender) on high speed for 1 to 2 minutes until smooth and creamy. (Allow the soup to cool slightly before pouring it into a blender to help prevent major splashes from the heat.)
Once pureed, strain the soup through a fine-mesh sieve for a smoother texture. Return the soup to the pot and add the milk and heavy cream. Simmer the soup over low heat for 10 to 15 minutes, stirring constantly to avoid sticking to the bottom. Add salt and ground black pepper to taste.
For serving, add one cup of roasted corn to the soup. Stir well and serve either hot or chilled, garnished with freshly chopped parsley and a drizzle of heavy cream on top.