Scrub potatoes under cold water and pat completely dry—this matters because moisture on the skin prevents browning. Cut each potato lengthwise into four thick wedges, keeping the skin on. I always leave the skin because it holds everything together while the inside gets tender, plus it tastes better than you'd expect.

Bring a large pot of salted water to a rolling boil. Add wedges and cook for 8-10 minutes until a fork slides through with slight resistance. You want them partially cooked, not soft—this is my most important confession because I used to skip this step and ended up with burnt exteriors and raw centers. The par-boiling prevents that disaster.

Drain wedges in a colander and let them cool for 5 minutes. While they cool, combine olive oil, salt, black pepper, smoked paprika, dried rosemary, minced garlic, and cayenne pepper in a small bowl. The reason you mix seasonings in oil first is so they coat evenly instead of settling to the bottom and burning on the grill.

Pat wedges with a clean kitchen towel to remove excess moisture. Toss them gently in the seasoned oil mixture until every cut surface gleams. Don't skip this coating step because you need those herbs and spices pressed directly onto the flesh where heat will build flavor.

Heat your grill to medium-high heat (about 400°F). Oil the grates well with a paper towel dipped in oil—burnt-on potato sticks if you skip this. Place wedges cut-side down and let them sit undisturbed for 3-4 minutes until golden char marks appear. I know it's tempting to flip constantly, but those char marks are flavor.

Flip each wedge and place a small pat of butter on the grilled side. Continue cooking for another 3-4 minutes on the skin side. The butter melts into the crevices and creates this rich, almost nutty sweetness that finishes beautifully. You'll smell it when it's ready—that's your cue.

Transfer wedges to a serving platter while still warm. Scatter the shredded cheese over top, then add fresh parsley and lemon zest. The heat will slightly soften the cheese without melting it completely, which is exactly what you want for that contrast between creamy and firm.