Melt the butter in a small saucepan over medium-low heat, then add the freshly minced garlic and cook for about 1 minute until fragrant—this blooms the garlic's flavor into the butter. Stir in the cajun seasoning, fresh thyme, and black pepper, then remove from heat and set aside. While the butter infuses, cut the potatoes into bite-sized pieces (about 1 to 1.5 inches), cut the corn into 1-inch thick rounds, cut the sausage into 1-inch rounds, and pat the shrimp dry with paper towels—dry shrimp will grill better and develop better color. I like to use Kerrygold butter and quality smoked sausage because they really elevate the final dish with richer flavor.
Bring a large pot of salted water to a boil and add the cut potatoes, cooking for about 8-10 minutes until they're just beginning to soften but still have some firmness in the center. Add the corn rounds to the pot and continue cooking for another 4-5 minutes—the vegetables should be partially cooked but not fully tender since they'll finish cooking on the grill. Drain the vegetables in a colander and let them cool slightly while you prepare the skewers.
Thread the parboiled potatoes, corn, shrimp, and sausage pieces alternately onto skewers, dividing the ingredients evenly among them—aim for about 4-5 pieces of each ingredient per skewer. Leave a small gap between pieces so heat can circulate and cook everything evenly. I prefer to start and end with a potato piece as it acts as a buffer and helps hold everything in place.
Preheat your grill to medium-high heat and lightly oil the grates. Lay the assembled kabobs on the grill and cook for 3-4 minutes on the first side until you see light char marks. Flip the kabobs, brush generously with the cajun butter mixture from Step 1, then cook for another 3-4 minutes. Flip once more, brush with more butter, and cook until the shrimp are opaque and pink and the sausage has light char marks—total cooking time should be around 7-8 minutes. The shrimp will cook quickly, so watch them carefully to avoid overcooking.
Transfer the grilled kabobs to a serving platter and finish with a sprinkle of fresh parsley. Serve immediately with lemon wedges on the side so guests can squeeze fresh citrus over their kabobs for brightness that cuts through the rich, buttery cajun flavors.