Place the oven rack about 6 inches below the broiler and preheat the broiler to high. Arrange the whole peppers on a baking sheet and broil for 15 to 20 minutes, turning every few minutes until the skins are blackened and blistered on all sides.
Transfer the peppers to a bowl and cover tightly with a plate or plastic wrap. Let them steam for 10 minutes. Peel away the skins, remove the stems and seeds, and roughly chop the peppers.
While the peppers cool, heat the olive oil in a Dutch oven over medium heat. Add the onion and cook for 6 to 8 minutes until softened. Stir in the garlic and cook for another minute.
Add the tomato paste, smoked paprika, oregano, and crushed red pepper flakes. Cook for 1 minute, stirring constantly, until fragrant.
Stir in the roasted peppers, cannellini beans, and vegetable broth. Bring the soup to a gentle simmer and cook for 15 minutes.
Remove the pot from the heat. Add the basil and lemon juice, then blend the soup until completely smooth using an immersion blender. If using a countertop blender, blend in batches and return the soup to the pot.
Season with salt and pepper to taste. If the soup is thicker than you’d like, stir in a little extra vegetable broth until it reaches your preferred consistency.
Ladle into bowls and finish with a swirl of vegan cream, fresh basil, cracked black pepper, and a pinch of red pepper flakes. Serve warm with grilled sourdough or garlic basil toast.