Cut the Yukon Gold potatoes into halves or slices about ½-inch thick—this thickness allows them to cook through while developing a nice crust on the grill. In a large bowl, combine the potatoes with salt, lemon pepper, minced garlic, dried oregano, and fresh thyme sprigs. Drizzle with extra virgin olive oil and squeeze the lemon wedge over everything, tossing gently but thoroughly to coat all surfaces evenly. Let this sit for 5-10 minutes while you preheat the grill—this brief rest allows the potatoes to absorb the flavors.

Heat your grill to medium-high heat (around 375-400°F if using a gas grill). Arrange the seasoned potatoes from Step 1 in a single layer on a grill tray or directly on grill grates, placing them cut-side down to develop a golden, caramelized crust. Grill for 20-25 minutes total, checking halfway through—if the cut sides are browning too quickly and the potatoes still feel firm inside, flip them to cook the skin side. I like to give the potatoes a gentle shake every few minutes to ensure even cooking and prevent sticking. The potatoes are done when they're fork-tender inside and have deep golden-brown edges.

Transfer the grilled potatoes to a serving platter while still warm. Scatter the feta cheese crumbles over the top, allowing them to slightly soften from the heat of the potatoes. Serve immediately while the potatoes are at their peak temperature and the lemon-herb flavors are most vibrant.