For the basil vinaigrette: Add the olive oil, lemon juice, basil and shallot to the carafe of a blender. Blend until the shallot is broken down and the ingredients are thoroughly combined. Taste and season with salt and pepper. Blend once more to combine the seasonings. Transfer to a serving vessel alongside the salad.
For the salad: Add the arugula to a large serving platter. Sprinkle with the chives, mint and parsley. Then sprinkle with the lemon zest and peas. Distribute the burrata evenly on top. Sprinkle with the flaky salt and serve with the basil vinaigrette on the side.