Tear an 18” piece of heavy-duty foil for each packet, along with a 16” sheet of parchment paper for each. Layer the parchment paper on top of the foil.
Divide the corn, zucchini, minced garlic, shrimp, spices, and butter between the two sheets of foil.
To form the packets, bring one of the short edges of the foil to meet the other, then crimp around all edges to seal.
Cook the packets on a grill (or the grill grate over your campfire) for 8 minutes, flipping occasionally.
Remove from the grill and let cool slightly. Open the packets carefully - they will be full of hot steam. Top with fresh parsley and enjoy.