Start by preparing all your vegetables: husk and cut the corn into 2-inch rounds, cut potatoes into 1-inch cubes, slice carrots into 1/2-inch coins, slice zucchini into 3/4-inch half moons, and cut the red onion into 1-inch wedges. In a small bowl, combine the butter, mustard, smashed garlic cloves, thyme, salt, black pepper, and smoked paprika—this seasoned butter base will coat everything evenly and develop rich flavor as it melts during grilling. I like to prepare all my vegetables first so they're ready to toss, which keeps the whole process moving smoothly.
In a large bowl, combine all the prepared vegetables: corn, potatoes, carrots, zucchini, and onion. Pour the seasoned butter mixture from Step 1 over the vegetables and toss everything together until all pieces are evenly coated. Make sure the harder vegetables like potatoes and carrots get good coverage since they need the most cooking time. For better flavor distribution, I give it a good 1-2 minute toss to ensure every piece gets some of that mustard-butter coating.
Tear off four large sheets of heavy-duty aluminum foil (about 12x18 inches each). Divide the coated vegetable mixture evenly among the four sheets, placing it in the center of each piece. Fold the foil over the vegetables and crimp the edges tightly to create sealed packets, leaving a little headspace inside for steam to circulate. Make sure the seams are facing up when you place them on the grill—this helps any condensation drain away from the vegetables rather than pooling around them.
Heat your grill to medium heat (around 375-400°F if you have a thermometer). Carefully place all four foil packets on the grill grates with the seam side facing up. Grill for 25-35 minutes, depending on how hot your grill runs and the size of your vegetable pieces—the potatoes are your indicator; they should be fork-tender when done. You can carefully open one corner of a packet to peek inside around the 25-minute mark to check doneness.
Carefully remove the hot foil packets from the grill using tongs or heat-resistant gloves—they'll be very hot! Place each packet on a plate or serving board and open by carefully peeling back the foil away from you to avoid steam burns. Serve immediately while everything is hot and steaming, and if you like, drizzle any accumulated juices from the foil back over the vegetables for extra flavor.