Slice each large sweet onion into 3/4-inch thick rounds. To keep the rounds intact during grilling, push a metal skewer through the center of each round, positioning it about 3/4 inch from the root end. This skewer will hold the onion layers together as they cook and make flipping easier. Once all rounds are skewered, trim any excess skewer length that extends beyond the onion so it doesn't interfere with grilling.

Brush both sides of each skewered onion round generously with extra virgin olive oil, making sure the oil coats all exposed surfaces—this helps them develop a nice caramelized crust. Sprinkle both sides evenly with kosher salt and freshly ground black pepper, then finish with the dried thyme. I like to season the onions right before grilling rather than ahead of time, as the salt can draw out moisture and make them soggy if left sitting too long.

Prepare your grill for two-zone cooking by heating one side to medium-high heat and leaving the other side cooler or with no direct flame. This two-zone setup lets you start the onions on the cool side to cook gently without burning, then move them to higher heat if needed for final caramelization. Let the grill preheat for 5-10 minutes until it reaches temperature and the grates are hot enough that water droplets sizzle immediately.

Place the seasoned onion skewers on the cool side of the grill to cook slowly and develop sweetness without charring too quickly. Cook for 25-40 minutes total, flipping every 10-15 minutes to ensure even cooking and caramelization on both sides. The onions are done when they're completely tender and pull apart easily with a fork, with the edges and flat surfaces nicely caramelized and slightly charred. I find that smaller onions cook faster while larger ones may need closer to 40 minutes, so check for tenderness rather than relying solely on time.

Transfer the grilled onions to a serving plate or board and drizzle with balsamic glaze while they're still warm. The warmth helps the glaze coat the onions evenly and brings out the sweet and slightly tart flavors that complement the caramelized sweetness of the grilled onions perfectly.