Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Spray the grill with vegetable oil cooking spray.
For the pesto: Pulse the basil, nuts, lemon juice, garlic, lemon zest, salt and pepper until finely chopped in a blender or food processor. With the machine running, gradually add the oil until the mixture is smooth and thick. Add the cheese and pulse until just incorporated. Season with salt and pepper.
Thread 1 round of zucchini onto a skewer. Thread 1 crumpled piece of prosciutto onto the skewer. Repeat 3 more times ending with a round of zucchini. Each skewer should have 5 rounds of zucchini and 4 pieces of prosciutto. Drizzle the skewers with olive oil and grill, turning occasionally, until the zucchini are tender, about 5 minutes.
Brush the skewers with the pesto, using a pastry brush, and serve.