Place an oven rack in the center of the oven. Preheat the oven to 350 degrees F.
Line a baking sheet with parchment paper. Place the prosciutto in a single layer on the prepared baking sheet. Bake for 12 to 14 minutes until crispy. Drain on paper towels. Chop the prosciutto into 1/4-inch pieces.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. In a medium bowl, toss together the asparagus and 2 teaspoons olive oil. Season with salt and pepper. Grill for 2 to 3 minutes each side until crisp-tender.
In a medium bowl, combine the lemon juice and 2 tablespoons olive oil. Whisk until combined. Season with salt and pepper, to taste. Add the melon and mozzarella cheese and toss until all ingredients are combined.
Arrange the asparagus on a platter. Using a slotted spoon, spoon the melon and burrata cheese on top of the asparagus. Drizzle any remaining vinaigrette over the top. Sprinkle the prosciutto and pine nuts on top and serve.
*Cook's Note: To toast pine nuts, arrange in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven for 8 to 12 minutes until lightly browned.