Preheat the oven to 400 degrees. Place the tomato halves and red pepper quarters on a baking sheet. Roast for 20 minutes until the edges begin to char.
Transfer the roasted tomatoes and peppers to the slow cooker. Add the diced onion, minced garlic, vegetable broth, oregano, smoked paprika, salt, and black pepper.
Cover and cook on low for 6 hours or on high for 3 hours.
Use an immersion blender to puree the soup until smooth. Stir in the heavy cream.
Ladle into bowls and top with fresh basil before serving.