Preheat the oven to 400F.
Place the bell peppers on a shallow oven tray and bake whole for 30 minutes until charred and soft.
Remove from oven and place in a bowl. Cover the bowl with plastic wrap. Let sit for 5 to 10 minutes. Once cool enough to handle, peel away the skin and remove the core and seeds.
In a large pot, heat the olive oil over medium heat. Add the onion and garlic. Cook until softened, about 5 minutes.
Roughly chop the cooked peppers and add to the pot along with chilli flakes and cayenne. Stir to combine.
Add the vegetable stock, salt, and pepper. Bring the soup to a boil, and then reduce heat to low and simmer for 10 minutes.
Transfer the soup to a blender, or use a stick blender and process until smooth.
Divide into 4 serving bowls. Garnish with sour cream and chopped basil.