Using a sharp knife peel the blood oranges and cut them into thin slices.
Pat dry the burrata cheese and using your fingers tear it into big pieces. Place on a serving platter and surround with the sliced blood oranges.
Make the basil pesto. Add the 2 cups of basil leaves, garlic, pine nuts and the olive oil to the bowl of a food processor. Process until smooth and transfer to a bowl.
Stir the parmigiano reggianno cheese into the pesto together with the lemon juice. Adjust seasonings to taste with sea salt and more lemon juice.
Spoon the basil pesto over the blood oranges and burrata, sprinkle with the pine nuts and garnish with the basil.