Lightly oil a grill set to medium-high heat. Season the chicken breasts with sea salt and freshly ground black pepper. Grill until done, 8 to 10 minutes, turning the chicken breasts halfway through. Let cool, then slice.
To make the dressing:
Place all the ingredients in a blender and blend until emulsified and smooth (the dressing will look like a loose pesto). Store in an airtight container.
To make the salad:
Break the balls of Mozzarina di Bufala cheese into pieces. Lay the grilled chicken, the Mozzarina di Bufala, and all the salad ingredients in a large shallow bowl or on a large serving plate. Drizzle some of the dressing all over. Serve immediately, with additional dressing on the side.