Place a medium soup pot or heavy saucepan over a medium heat. Add the olive oil, butter, onion, garlic, salt and pepper. Cook until the onions are soft and translucent, about 5 minutes.
Add the peas and basil, and heat until the peas are thawed.
Place the pea mixture in a blender. Add 250ml of the chicken broth and pulse until pureed, adding more broth, if necessary.
Return the pureed mixture to the pan. Stir in the remaining chicken broth and the cream. Return the pan to a medium heat and cook until hot, but not boiling.
To serve, place the soup in bowls. Float a thin slice of fresh mozzarella cheese on top of each bowl and sprinkle with the diced roasted red peppers. Serve immediately.