For the pesto: Preheat oven to 400° F. Spread pine nuts in a single layer on the bottom of a pie tin or cookie sheet and bake until golden brown; about 3 minutes. Combine arugula, Parmesan, olive oil and toasted pine nuts in a food processor; puree to a spreadable consistency.
For the vinaigrette: In a food processor, puree carrot tops, Dijon mustard and white balsamic vinegar until well combined. On low speed, slowly stream in the olive oil to emulsify; season to taste.
For the salad: In a large mixing bowl, toss vegetables with enough carrot top vinaigrette to coat. Check seasoning, and add salt and pepper to taste. On the bottom of eight chilled flat salad plates, spread a thin layer of the arugula pesto using a small offset spatula. Assemble the salads by arranging the carrots on the plate, and then adding asparagus tips, radish crudités, fava beans and sugar snap peas in a decorative fashion. In a medium mixing bowl, toss the arugula and Treviso leaves with carrot top vinaigrette to coat; check seasoning. Arrange lettuces on top of the vegetables. Arrange large pieces of fresh burrata cheese around the salads and serve chilled.