Preheat the broiler and line a baking sheet with foil. Place the peppers skin side up and broil for 10 to 12 minutes until the skins are blackened and blistered.
Transfer the peppers to a bowl, cover tightly and let them steam for 10 minutes. Peel off the skins and discard them.
Heat the olive oil in a large pot over medium heat. Add the onion and cook for 5 minutes, then stir in the garlic, smoked paprika and red pepper flakes for 1 minute.
Add the roasted peppers, tomatoes, broth and cashews. Bring to a boil, then simmer for 15 minutes until the cashews are soft.
Carefully transfer the soup to a high speed blender, venting the lid, and blend until completely silky. The simmered cashews create a rich, creamy texture without any cream.
Return the soup to the pot and stir in the balsamic vinegar, salt and pepper. Serve topped with fresh basil.