Preheat the oven to 400 degrees F (200 degrees C). Place a pizza stone in the oven to warm.
Mix zucchini, 2 tablespoons olive oil, jalapeno peppers, lemon juice, mint, salt, and pepper together in a bowl.
Stretch pizza dough onto the warmed stone; brush top of dough with remaining olive oil. Lay sliced Monterey Jack cheese on top; cover with zucchini mixture; arrange prosciutto slices on top. Sprinkle Parmesan cheese over pizza.
Bake in the preheated oven until crust is golden and cheese is melted, about 15 minutes.