Preheat the broiler. Use a sharp knife to make a slit through the shell along the back of each shrimp. Remove the vein, leaving the shell intact. Rinse and pat dry, then transfer to a large bowl.
Whisk 1/4 cup olive oil, the ginger, paprika, 2 teaspoons salt, and pepper to taste in a bowl. Add half of the dressing to the bowl with the shrimp and toss. Add the lemon and zucchini to the remaining dressing and toss, then spread on a large foil-lined baking sheet. Broil until the lemon and zucchini begin to brown, 5 to 7 minutes. Add the shrimp and broil until the shells are pink, about 3 minutes. Turn the shrimp, lemon and zucchini and broil 3 to 4 more minutes.
Whisk the remaining 1/4 cup olive oil, the parsley and a pinch of salt in a small bowl. Divide the shrimp, lemon and zucchini among plates and drizzle with the parsley oil. Serve with bread.