Set the oven to broil. Place the whole bell peppers and tomatoes on a baking sheet. Drizzle with 3 tablespoons of olive oil and turn to coat. Broil, turning the vegetables every 5 minutes, until their skins are charred.
After about 10 minutes, remove the tomatoes from the oven and set aside to cool. Continue broiling the bell peppers for another 10–15 minutes, or until softened and charred. Remove from the oven and let cool.
Once cool enough to handle, remove the stems, skins, and seeds from the bell peppers. Cut the peppers into roughly 3-inch pieces. Remove the cores from the tomatoes and cut them into roughly 2-inch pieces.
Heat a medium soup pot over medium heat and add the remaining olive oil. Add the sliced onions and sauté until softened. Stir in the dried oregano.
Add the roasted peppers and tomatoes, stirring to combine with the onions. Pour in the water, cover, and simmer over low heat for 15 minutes. Carefully transfer the mixture to a blender and puree until smooth. You can also use an immersion blender directly in the pot.
Return the pureed soup to the pot. Stir in the smoked paprika, salt, and heavy cream or half-and-half. Cover and simmer over low heat for another 15 minutes.