In a large saucepan over a medium heat, melt the butter then add the onions and pepper. Let the onions sweat, 10 to 15 minutes, reducing the heat if necessary to prevent browning, stirring frequently.
Add the vegetable stock, tomatoes, garlic, and the chilli flakes (I add loads of chilli flakes but you don't need to add a lot if you don't like it too spicy). Let the soup simmer gently, until the flavours of the garlic have completely infused throughout, 10 to 15 minutes.
Add the chopped anchovies and olives to the soup and let it continue simmering gently for another fifteen to twenty minutes.
All the ingredients should be beautifully infused by now. Use a hand held liquidiser to semi-blend the soup in the pan, or blend to your desired consistency. Ladle into warmed bowls and serve immediately!